We investigate the potential of surface plasmon polaritons at noble metal interfaces for surface-enhanced chiroptical sensing of dilute chiral drug solutions with nl volume. The high quality factor of surface plasmon resonances in both Otto and Kretschmann configurations enables the enhancement of circular dichroism differenatial absorption thanks to the large near-field intensity of such plasmonic excitations. Furthermore, the subwavelength confinement of surface plasmon polaritons is key to attain chiroptical sensitivity to small amounts of drug volumes placed around ≃100 nm by the metal surface. Our calculations focus on reparixin, a pharmaceutical molecule currently used in clinical studies for patients with community-acquired pneumonia, including COVID-19 and acute respiratory distress syndrome. Considering realistic dilute solutions of reparixin dissolved in water with concentration $\u22645$ mg/ml and nl volume, we find a circular-dichroism differential absorption enhancement factor of the order ≃20 and chirality-induced polarization distortion upon surface plasmon polariton excitation. Our results are relevant for the development of innovative chiroptical sensors capable of measuring the enantiomeric imbalance of chiral drug solutions with nl volume.

## I. INTRODUCTION

Chiral sensing plays a key role in pharmaceutics because the specific enantiomeric form of drugs affects their functionality and toxicity.^{1} Current state-of-the-art techniques capable of measuring enantiomeric excess of chiral mixtures, e.g., nuclear magnetic resonance,^{2} gas chromatography^{3} and high performance liquid chromatography,^{4} provide advanced tools for drug safety, but are designed to operate with macroscopic drug volumes and are not suitable for real-time analysis and innovative lab-on-a-chip integration schemes. Photonic devices can potentially overcome such limitations, but technological advancement in this direction is hampered by the inherently weak chiroptical interaction, which requires ml volumes in order to attain sensitivity to the enantiomeric imbalance of chiral drug solutions through, e.g., polarimetry^{5} or electronic/vibrational circular dichroism (CD).^{6,7} Diverse approaches are currently investigated to enhance chiroptical interaction, as in particular ultrafast and nonlinear chiroptical spectroscopy techniques^{8–11} or the exploitation of superchiral fields^{12,13} that can be engineered via metasurfaces and nanophotonic structures.^{14–16} However, the actual exploitation of superchiral fields for novel chiral sensing schemes remains elusive, mainly because most of the experimental sensing demonstrations in literature rely on chiral nanoplasmonic subtrates. The major issue is that when a chiral sample is placed in the near-field of such nanostructures, the detected CD signal is contaminated by the chiroptical response of the nanostructure itself, which acts as a strong background noise and masks the weak chiroptical signal of the actual sample.^{17} It has to be noted that chiral drugs diluted in solutions are continuously deformed by the conformational fluctuations of the molecule in interaction with the solvent at finite temperature, modulating over time their chiroptical response. Concurring electric and magnetic resonances in nanostructures provide enhanced CD thanks to the dual enhancement of both electric and magnetic fields.^{18} While such schemes are promising for single molecule chiral discrimination, they are difficult to implement for extended drug solutions because CD enhancement is attained only at specific hot spots where electric and magnetic field lines are strong, parallel and *π*/2 shifted.^{17,18} Over a complementary direction, metal-based nanophotonic structures enable plasmon-enhanced CD spectroscopy,^{19} which has been predicted for isolated molecules,^{20} while it has been adopted mainly to characterise chiral nanoparticles.^{21–23}

Here we predict that CD differential absorption (CDDA) by nl volumes of dilute drug solutions can get enhanced by a factor *f*_{CDDA} ≃ 20 via the excitation of surface plasmon polaritons (SPPs) at a planar interface between a noble metal and the chiral sample. In particular, we focus on an isotropic assembly of reparixin (an inhibitor of the CXCR2 function attenuating inflammatory responses^{24} that has been adopted in clinical trials for the treatment of hospitalized patients with COVID-19 pneumonia^{25}) dissolved in water with dilute number molecular density of the order $nmol=nmolR+nmolS\u224310\u22122$ nm^{−3} (corresponding to a concentration of 5 mg/ml), where $nmolR,S$ indicate the number densities of R and S enantiomers, respectively. Because SPPs possess a momentum greater than the one of radiation in vacuum, their excitation requires a radiation momentum kick, which can be provided either by a grating^{26,27} or by a prism through attenuated total reflection in Kretschmann^{28} or Otto^{29} configurations. However, the adoption of gratings to excite SPPs modifies significantly the SPP dispersion,^{30} and in turn here we focus on silica prism coupling. We observe that CDDA Δ*A* = *A*_{R} − *A*_{L} upon right/left circular polarization excitation is proportional to the enantiomeric excess density $\Delta nmol=nmolS\u2212nmolR$, and in turn by measuring the CDDA it is possible to retrieve Δ*n*_{mol}. Furthermore, we observe that the maximum plasmon-induced CDDA enhancement factor *f*_{CDDA} ≃ 20 is attained with silver in the Otto configuration, while other noble metals like gold and copper provide a smaller *f*_{CDDA}. The vacuum wavelength (*λ*) dependence of all macroscopic optical parameters [dielectric permittivity *ɛ*_{r}(*λ*), magnetic permeability *μ*_{r}(*λ*) and chiral parameter *κ*(*λ*)] of the isotropic chiral mixture are calculated from first principles. This is accomplished by perturbatively solving the density matrix equations accounting for the leading electronic and vibrational absorption peaks and by averaging the obtained polarizability tensors over the random molecular orientation through the Euler rotaton matrix approach.^{31,32} We evaluate plasmon-enhanced CDDA Δ*A* by classical electrodynamics calculations accounting for (i) silica prism in the Otto and Kretschmann SPP coupling schemes, (ii) the macroscopic bi-anisotropic response of the chiral mixture, and (iii) the dielectric response of noble metals. Our predictions of efficient plasmon-enhanced CDDA by isotropic drug solutions of nl volume suggest novel avenues for integrated chiroptical sensing.

For the present study, it is necessary to make use of quantum molecular observables (i.e., electric and magnetic moments, electronic and vibrational excitation energies) evaluated for the solvated drug, i.e., aqueous reparixin in our calculations. This is not a trivial task because such quantum molecular observables should be perceived as genuinely quantum expectation values averaged (in statistical-mechanical terms) over a large number of reparaxin/solvent configurations. For this purpose we have adopted a combination of computational approaches, described to some extent in the supplementary material and briefly illustrated in Fig. 1. The adopted methods combine semi-classical Molecular Dynamics (MD) simulations (necessary for the reparaxin-solvent conformational sampling), quantum-chemical (QM) calculations and Perturbed Matrix Method (PMM)^{33–35} which, using the information obtained from MD simulations and QM calculations, provides the observables of interests expressed as ensemble averages. This approach is necessary for including in our model subtle but relevant effects produced by the semi-classical atomic-molecular motions (both reparaxin and water).

## II. ELECTRONIC AND VIBRATIONAL STRUCTURE OF REPARIXIN IN WATER

*b*

_{k}, where

*k*= 1 − 4, located through MD simulations and ED analysis and depicted in Fig. 2 in the case of reparixin S enantiomer. We underline that, due to selection rules, we consider only two vibrational states (labelled by the index

*ν*= 0, 1) producing resonant interaction with external radiation in the mid-infrared (mid-IR) with vibrational energy

*ℏω*

_{v}independent over the reparixin conformation state

*k*. Indeed, we found that

*ℏω*

_{v}is practically unaffected by the molecular configuration state, i.e., the nature of the vibrational mode (calculated as described in the supplementary material) coincides in the four conformation states. For every enantiomer labelled by the index

*a*= R, S, the radiation-unperturbed vibronic structure is approximated by independent electronic/vibrational Hamiltonians $H\u03020el,vib(k,a)$, given by

*ℏω*

_{i}(

*k*) and

*ℏω*

_{v}(

*ν*+ 1/2) are the electronic/vibrational energy eigenvalues with eigenstates |

*i*(

*k*,

*a*)⟩ and |

*ν*(

*a*)⟩. For flexible solvated molecules such as reparixin, the effect of the vibronic transitions in the UV spectral shape is negligible if compared to the one produced by the chromophore and solvent conformational transitions. In turn, the lack of fine structure in the electronic transitions is due to the effect of the semi-classical molecular vibrations and solvent perturbations producing a spectral broadening that prevents their observation. Furthermore, we account only for the electronic states

*i*= 1 − 5 because we find that the corresponding energy levels are the only ones producing resonant electronic absorption peaks in the ultraviolet (UV). Figure 2(b) illustrates the schematic vibronic structure of reparixin for a generic molecular conformation state. In the electric/magnetic dipole approximation, the molecule interacts with external radiation through the electronic/vibrational perturbing Hamiltonians given by the expressions

**E**(

**r**,

*t*),

**B**(

**r**,

*t*) are the external radiation electric and magnetic induction fields and

**m**

^{01}requires going beyond the Born-Oppenheimer approximation, see supplementary material for additional details. Note that transition electric dipole moments are real polar vectors $u(k,a)\u2208R3$, while transition magnetic dipole moments are purely imaginary axial vectors $w(k,a)\u2208I3$, where we indicate with

**u**(

*k*,

*a*) either

**d**

_{1i}(

*k*,

*a*) or

**d**

^{01}(

*a*), and with

**w**(

*k*,

*a*) either

**m**

_{1i}(

*k*,

*a*) or

**m**

^{01}(

*a*), depending over the electronic/vibrational dynamics considered. We define the reflection operator $Rn\u0302=I\u22122n\u0302n\u0302$ by the plane perpendicular to the unit vector $n\u0302$ where reflection symmetry is broken. Transition dipole moments of opposite enantiomers can be calculated by applying the reflection operator: $u(k,S)=Rn\u0302u(k,R)$, $w(k,S)=\u2212Rn\u0302w(k,R)$. In turn, while the modulus of the transition dipole moments is unaffected by the enantiomeric type |

**u**(

*k*, S)| = |

**u**(

*k*, R)|, |

**w**(

*k*, S)| = |

**w**(

*k*, R)|, the scalar product

**u**(

*k*, S) ·

**w**(

*k*, S) = −

**u**(

*k*, R) ·

**w**(

*k*, R) flips sign for opposite enantiomeric forms. Such a quantity, which we call

*chiral projection*, is in turn chirally sensitive as it involves the scalar product of a polar and an axial vector. In Fig. 2(c) we report the MD-induced temporal evolution of electronic contributions |

**d**

_{12}|, |

**m**

_{12}| and the modulus of the chiral projection |

**d**

_{12}·

**m**

_{12}| of the S reparixin enantiomer in conformation state

*k*= 1. Note that such quantities, constituting the key microscopic ingredients producing optical activity, see below, depend over time due to MD. For this reason, in our quantum-mechanical calculations of the macroscopic bi-anisotropic response we use ensemble-averaged ⟨|

**d**

_{12}|⟩, ⟨|

**m**

_{12}|⟩ and ⟨|

**d**

_{12}·

**m**

_{12}|⟩ (calculated as time-averages over the ≃ns MD timescale in our ergodic assumption, see below.

## III. MACROSCOPIC BI-ANISOTROPIC RESPONSE OF REPARIXIN IN WATER

*k*and enantiomeric form

*a*, radiation-induced electron/vibrational dynamics of chiral drugs (reparixin in our calculations) is in turn governed by the density matrix equations

*λ*= 2

*πc*/

*ω*, where

*c*is the speed of light in vacuum and

**V**=

**E**,

**B**, respectively, Eq. (4) is solved perturbatively at first-order yielding $\rho \u0302k,ael,vib(r,t)$.

^{36}The expectation value of the induced electric/magnetic dipole moments expressed as an ensemble average considering all the reparaxin conformation states for each enantiomer form

*a*(see Fig. 1), is in turn given by $oael,vib=\u2211k=14p(k)Tr\rho \u0302k,ael,vibo\u0302(k,a)$, where

*p*(

*k*) = 0.25, see Fig. 2(a), and

**o**=

**d**,

**m**, respectively. Owing to the random molecular orientation, the induced electric/magnetic dipole moments averaged over arbitrary rotations through the Euler rotation matrix approach

^{31,32}are given by the expressions

*ɛ*

_{0},

*μ*

_{0}are the vacuum permittivity and permeability, respectively, and

*α*

_{e}(

*ω*),

*α*

_{b}(

*ω*), $\alpha m(a)(\omega )$ are the linear isotropic electric, magnetic and mixing polarizabilities of every molecular enantiomer, given by the expressions

*p*(

*k*) = 0.25, $Ce(vib,\u2009el)=2\u27e8|D(vib,\u2009el)|2\u27e9/3\u210f$, $Cb(vib,\u2009el)=2\u27e8|M(vib,\u2009el)|2\u27e9/3\u210f$ and $Cm(vib,\u2009el)=2i\u27e8Im[D(vib,\u2009el)\u22c5M(vib,\u2009el)]\u27e9/3\u210f$, where ⟨(⋯)⟩ indicates the ensemble-average (calculated as time-average over the ≃ns MD time-scale in our ergodic assumption), $D(vib)=d01$, $Dj(el)=d1j$, $M(vib)=m01$ and $Mj(el)=m1j$. The angular frequency dependence of the polarizabilities is accounted by $F(vib)(\omega )=\u2211\sigma =\xb11\sigma /(\omega +\sigma \u27e8\omega v\u27e9+i\gamma v/2)$ and $Fj,k(el)(\omega )=\u2211\sigma =\xb11\sigma /[\omega +\sigma \u27e8\omega j(k)\u2212\omega 1(k)\u27e9+i\gamma j(e)(k)/2]$, where

*γ*

_{v}= 0.012 fs

^{−1}is the relaxation rate of the only reparixin vibrational transition

*ν*= 0 → 1 with energy

*ℏω*

_{v}= 0.218 eV (corresponding to the transition wavelength

*λ*= 5.69

*μ*m). The calculated electric/magnetic transition dipole moments

**d**

^{01},

**m**

^{01}provide $\u27e8|d01|2\u27e9/d0=0.105$, $\u27e8|m01|2\u27e9/m0=0.398$ and ⟨Im[

**d**

^{01}(S) ·

**d**

^{01}(S)]⟩/

*d*

_{0}

*m*

_{0}= 0.007, where

*d*

_{0}= |

*e*|

*a*

_{0},

*a*

_{0}=

*ℏ*/

*m*

_{e}

*cα*is the Bohr radius,

*m*

_{0}= |

*e*|

*ℏ*/2

*m*

_{e}is the Bohr magneton,

*α*is the fine-structure constant and

*e*,

*m*

_{e}are the electron charge and mass. The electronic relaxation rates $\gamma j(e)$ have been extracted by the frequency bandwidth of the UV absorption spectrum and are reported in Table S1 along with the electronic transition energies, the electric/magnetic transition dipole moment moduli and the chiral projections expressed as ensemble averages. While in principle such a procedure might provide inconsistent results, we find that averaging over time the full microscopic polarizabilities (we calculate ensemble averages as time averages in our ergodic assumptions) or adopting individually averaged electric/magnetic transition dipole moduli, chiral projections and transition energies provides consistent results, see Fig. S1 for comparison.

^{31,32}electric/magnetic induced dipole moments ⟨

**d**

_{a}⟩, ⟨

**m**

_{a}⟩ and the number molecular densities $nmol(R,S)$ of the two enantiomeric forms

*a*= R,S. In turn, the macroscopic displacement vector

**D**(

**r**,

*t*) =

*ɛ*

_{0}

**E**(

**r**,

*t*) +

**P**(

**r**,

*t*) and magnetic field

**H**(

**r**,

*t*) =

**B**(

**r**,

*t*)/

*μ*

_{0}−

**M**(

**r**,

*t*) are given by the bi-anisotropic dispersion relations

*μ*

_{r}(

*λ*) = 1 +

*μ*

_{0}

*n*

_{mol}

*α*

_{b}(

*λ*) is the relative magnetic permeability of the chiral mixture (see supplementary material, where we report a MATLAB script for the calculation of

*ɛ*

_{r},

*μ*

_{r}and

*κ*).

Because the mixing polarizability flips sign for opposite enantiomers, $\alpha m(R)=\u2212\alpha m(S)$, the chiral parameter is proportional to the enantiomeric number density imbalance $\Delta nmol=nmol(S)\u2212nmol(R)$. Hence, optical activity vanishes for racemic mixtures where $nmol(R)=nmol(S)$. Note that $\epsilon r(\lambda )=\epsilon H2O(\lambda )+\Delta \epsilon r(\lambda )$ accounts for both the dielectric permittivity of the solvent (water) $\epsilon H2O(\lambda )$^{37} and the calculated correction produced by reparixin Δ*ɛ*_{r}(*λ*). In Figs. 3(a)–3(f) we illustrate the dependence of Δ*ɛ*_{r}(*λ*), *κ*(*λ*) and *μ*_{r}(*λ*) of a solution of pure S reparixin enantiomers dissolved in water $(nmol(R)=0)$ over the molecular number density *n*_{mol} and the vacuum wavelength of impinging radiation *λ*. Note that the chiroptical response of reparixin is affected by the tails of electronic (resonant at *λ* ≃ 250 nm) and vibrational transitions (resonant at *λ* ≃ 6 *μ*m). The real part of *ɛ*_{r}(*λ*) is the leading contribution to the refractive index dispersion $n(\lambda )=Re\epsilon r(\lambda )$, which is dominated by the refractive index of water due to the dilute molecular number density 10^{−3} nm^{−3} < *n*_{mol} < 10^{−1} nm^{−3}, see Figs. 3(a) and 3(d). The chirally insensitive extinction coefficient $kext(\lambda )=Im\epsilon r(\lambda )$ is affected mainly by the imaginary part of *ɛ*_{r}(*λ*) and is also dominated by the absorption of water, see Figs. 3(a) and 3(d). The relative magnetic permeability *μ*_{r}(*λ*) arises from the reparixin magnetic response but is chirally insensitive and provides only a tiny correction to the mixture absorption and dispersion, see Figs. 3(b) and 3(e). The dependence of the complex dimensionless chiral parameter *κ*(*λ*) over vacuum wavelength *λ* and molecular number density *n*_{mol} is depicted in Figs. 3(c) and 3(f). Note that the chiral parameter is responsible for the rotatory power (proportional to Re[*κ*(*λ*)]) and CD (proportional to Im[*κ*(*λ*)]), and is maximised at the electronic/vibrational resonances of reparixin.

## IV. PLASMON-ENHANCED CD SPECTROSCOPY

*d*(100 nm $<d<1\mu $m) embedding the chiral drug solution to be analysed, reparixin dissolved in water in our calculations. We consider monochromatic radiation with vacuum wavelength

*λ*, incidence angle

*θ*and arbitrary polarization given by the superposition of right (

*s*= +1) and left (

*s*= −1) circular components, impinging from a BK7 silica prism with relative dielectric permittivity

*ɛ*

_{g}(

*λ*)

^{38}(

*z*< 0, see Fig. 4(a) on a layer of reparixin dissolved in water [with bi-anisotropic response given by Eqs. (7a) and (7b)] placed at 0 <

*z*<

*d*and a metal substrate with dielectric constant

*ɛ*

_{m}(

*λ*) in

*z*>

*d*. Because circular polarization waves are eigenfunctions of Maxwell’s equations in the considered chiral medium, we decompose the impinging wave on circular polarization unit vectors $e\u0302s(0)(\theta )=(cos\u2061\theta e\u0302x+ise\u0302y\u2212sin\u2061\theta e\u0302z)/2$ and investigate the scattering dynamics of circular polarization waves by analytically solving macroscopic Maxwell’s equations accounting for the distinct polarization and magnetization fields in every medium of the considered geometry. We obtain

*z*) is the Heaviside step function, Θ

_{in}(

*z*) = Θ(

*z*) − Θ(

*z*−

*d*),

*ω*= 2

*πc*/

*λ*is the angular frequency,

*k*

_{0}=

*ω*/

*c*, $E0,\xb11(o)$ are the projections of the impinging vectorial amplitude over $e\u0302\xb11(0)$, $e\u0302s(R)=(\u2212cos\u2061\theta e\u0302x+ise\u0302y\u2212sin\u2061\theta e\u0302z)/2$, $kx=k0\epsilon gsin\u2061\theta $ is the conserved impinging

**k**-vector

*x*-component, $\beta s=k02(\kappa \u2212s\epsilon r\mu r)2\u2212kx2$ is the polarization-dependent wave-vector

*z*-component leading to optical activity and $kg,\u2009m=k02\epsilon g,m\u2212kx2$. In order to calculate the

*s*-dependent forward (

*σ*= +1) and backward (

*σ*= −1) amplitudes within the chiral medium $E\sigma ,s(o)$, the reflected $(ER,s(o))$ and transmitted $(ET,s(o))$ field amplitudes, we apply the boundary conditions (BCs) for the continuity of (i) the normal components of the displacement vector and induction magnetic field, and (ii) the tangential components of the electric and magnetic fields at the interfaces

*z*= 0,

*d*. Such BCs provide an 8 × 8 inhomogeneous system of algebraic equations for the field amplitudes, see Eq. (S1) in the supplementary material, which we invert numerically, obtaining $ER,\xb11(o),ET,\xb11(o)$ for any impinging field components $E0,\xb11(o)$. Note that, for racemic mixtures such that $nmol(S)=nmol(R)$ and

*κ*= 0, electromagnetic excitations of the system, see Fig. 4(a), can be split into independent transverse magnetic (TM) and transverse electric (TE) components. Conversely, owing to the chirality of reparixin enantiomers, non-racemic mixtures such that $nmol(S)\u2260nmol(R)$ produce mixed polarization dynamics. The absorbance of the system upon right (

*s*= +1, $E0,\u2212(o)=0$) and left (

*s*= −1, $E0,+(o)=0$) circular polarization excitation is in turn given by $As(o)(\theta ,\lambda )=1\u2212\u2211\sigma =\xb11|ER,\sigma (o)|2/|E0,s(o)|2$, from which we calculate the CDDA $\Delta A(o)(\theta ,\lambda )=A+(o)\u2212A\u2212(o)$. The TM absorbance $ATM(o)(\theta ,\lambda )=1\u2212\u2211\sigma =\xb11|ER,\sigma (o)|2/|E0|2$ is obtained by calculating $ER,\sigma (o)$ for TM impinging polarization, i.e., $E0,+(o)=E0,\u2212(o)=E0$. In Fig. 4(b) we depict the dependence of $ATM(o)$ over

*λ*,

*θ*considering silver as a metal substrate. Note that the absorbance is maximised at the SPP excitation curve

*A*

^{(k)}as a function of

*λ*,

*θ*. For right/left circular polarization excitation, also a Fabry-Perot resonance is excited at 600 nm $<\lambda <800$ nm and 50° <

*θ*< 60°, which enhances CDDA by a factor

*f*

_{CDDA}≃ 10.

## V. DISCUSSION

*θ*is depicted in Figs. 5(a)–5(c) at

*λ*= 700 nm for a silver substrate. At the SPP excitation angle

*θ*

_{SPP}≃ 70° polarization modulation is maximised for both circular and TM excitation polarization. Moreover, at

*θ*≃ 50° polarization dynamics is also enhanced due to Fabry-Perot resonance of solvated reparixin. Such a phenomenon does not occur when the drug solution is probed in the Kretschmann coupling scheme, schematically depicted in Fig. 6(a). Here, analytical solutions of Maxwell’s equations provide

*s*= +1, $E0,\u2212(k)=0$) and left (

*s*= −1, $E0,+(k)=0$) circular polarization excitation is given by $As(k)(\theta ,\lambda )=1\u2212\u2211\sigma =\xb11|ER,\sigma (k)|2/|E0,s(k)|2$, from which we calculate the Kretschmann CDDA $\Delta A(k)(\theta ,\lambda )=A+(k)\u2212A\u2212(k)$. Similarly to the Otto coupling scheme, the TM absorbance $ATM(k)(\theta ,\lambda )=1\u2212\u2211\sigma =\xb11|ER,\sigma (k)|2/|E0|2$ is obtained by calculating $ER,\sigma (k)$ for TM impinging polarization, i.e., by setting $E0,+(k)=E0,\u2212(k)=E0$. In Figs. 6(b) and 6(c) we depict the dependence of (b) $ATM(k)$ and (c) Δ

*A*

^{(k)}over

*λ*,

*θ*considering a silver thin film with thickness

*d*

_{m}= 80 nm. Note that, similarly to the Otto coupling scheme, the TM absorbance and the CDDA are maximised at the SPP excitation curve

*θ*

_{SPP}(

*λ*), indicated by the white lines in Figs. 6(b) and 6(c). Conversely to the Otto coupling scheme, Fabry-Perot resonances are not excited due to the intermediate metallic film. However, polarization dependent total interal reflection between glass and aqueous reparixin produces a CDDA absorption peak at

*θ*≃ 61°. It is worth emphasizing that such a phenomenon occurs only thanks to the sub-wavelength metallic thickness

*d*

_{m}≪

*λ*, enabling effective evanescent coupling between glass and aqueous reparixin. Also, note that the Kretschmann CDDA is about two orders of magnitude smaller than the Otto CDDA for identical total molecular number density

*n*

_{mol}and enantiomeric number density imbalance Δ

*n*

_{mol}. We illustrate the dependence of the Kretschmann Stokes parameters ($S0(k)=|ER,+(k)|2+|ER,\u2212(k)|2$, $S1(k)=2Re[ER,+(k)ER,\u2212(k)*]$, $S2(k)=\u22122Im[ER,+(k)ER,\u2212(o)*]$, $S3(k)=|ER,+(k)|2\u2212|ER,\u2212(k)|2$) over the incidence angle

*θ*in Figs. 6(d)–6(f) at

*λ*= 700 nm for a silver thin film with thickness

*d*

_{m}= 80 nm and a chiral medium with

*n*

_{mol}= 10

^{−2}nm

^{−3}and Δ

*n*

_{mol}=

*n*

_{mol}. Again, note that the Stokes parameters modulation is much weaker in the Kretschmann coupling scheme, similarly to CDDA.

In order to quantify the plasmon-induced CDDA enhancement, we define the factor *f*_{CDDA}(*λ*) = max_{θ}|Δ*A*^{(o,k)}(*θ*, *λ*)|/|Δ*A*_{bulk}(*λ*)|, where $\Delta Abulk(\lambda )=e\u22122Im\beta \u2212(b)d\u2212e\u22122Im\beta +(b)d$ is the absorbance of a layer of reparixin dissolved in water in the absence of the nanophotonic structure and $\beta \xb1(b)=k0(\epsilon r\mu r\u2213\kappa )$. In Figs. 7(a)–7(c) we depict the vacuum wavelength dependence of the CDDA enhancement for silver, gold and copper interfaces in the Otto coupling scheme. Note that the maximum plasmon-induced CDDA enhancement *f*_{CDDA} ≃ 20 is attained in the Otto configuration at *λ* ≃ 400 nm adopting silver as metal substrate, see Fig. 7(c). However, for *λ* > 500 nm, gold and copper provide CDDA enhancement factors *f*_{CDDA} ≃ 5 comparable with silver. We emphasize that, by assuming metal substrate lateral dimensions of the order of 1 × 1 mm^{2}, the considered chiroptical interaction volume is *V*_{int} ≲ 1 nl and the observed ≃10^{−6} CDDA can be readily measured using lock-in amplifiers. For the considered dilute molecular number density *n*_{mol} ≃ 10^{−2} nm^{−3}, we find that plasmon-enhanced CD spectroscopy is a viable chiroptical sensing platform able to discern ≲10^{13} R, S enantiomers in the considered *V*_{int}. We note that, in the considered Otto and Kretschmann coupling schemes, the transmitted intensity vanishes due to absorption because we assumed infinitely extended metal/chiral-sample for *z* > *d*, *d*_{m}. However, in practical experimental realizations, the physical dimensions of the metal/chiral-sample is finite and the transmitted intensity is non-vanishing. In turn, experimentally, absorbance can be measured as *A* = 1 − *I*_{R}/*I*_{0} − *I*_{T}/*I*_{0}, where *I*_{R,T,0} indicate the measured reflected (*I*_{R}), transmitted (*I*_{T}), and impinging (*I*_{0}) intensities. CDDA can be in turn measured as the absorbance difference upon left/right impinging polarization. The dissymmetry factor can be measured as the CDDA divided by the averaged absorbance upon left and right impinging polarization. We emphasize that, while the CDDA is enhanced due to SPP excitation, the dissymmetry factor remains unaffected by the nanostructure. Indeed, the role played by SPPs lies in the enhancement of the local electric field enabling both higher averaged absorbance and higher CDDA, while maintaining their ratio (dissymmetry factor) unaffected. In turn, the proposed CD spectroscopic schemes are distinct from superchirality approaches^{12–16} aiming at enhancing the dissymmetry factor. Nevertheless, importantly the enhanced CDDA enables reducing the volume of the drug solution to be analysed, as illustrated above.

## VI. CONCLUSIONS

We have investigated the potential of SPPs at interfaces between noble metals and a water solution of reparixin for plasmon-enhanced CD spectroscopy. The considered drug solution is composed of a realistic molecule adopted in clinical studies for patients with community-acquired pneumonia, including COVID-19 and acute respiratory distress syndrome. Our calculations of reparixin microscopic observables are based on MD simulations, TD-DFT and PMM simulations enabling the evaluation of time-averaged permanent and transition electric/magnetic dipole moments. Macroscopic optical parameters of the isotropic chiral mixture are calculated by perturbatively solving the density matrix equations. Our results indicate that SPP excitation enables plasmon-induced CDDA enhancement of the order *f*_{CDDA} ≃ 20 of solutions with sub-nl volume. Our results are relevant for the development of innovative integrated schems for chiroptical sensing of drug solutions.

## SUPPLEMENTARY MATERIAL

See the supplementary material for the theoretical details on the reparixin quantum observables calculations, the system of algebraic equations for field amplitudes in the Otto and Kretschmann configurations, and a MATLAB script for the calculation of the macroscopic bi-anisotropic response of reparixin dissolved in water.

## ACKNOWLEDGMENTS

This work has been partially funded by the European Union - NextGenerationEU under the Italian Ministry of University and Research (MUR) National Innovation Ecosystem Grant No. ECS00000041 - VITALITY - CUP E13C22001060006, the Progetti di ricerca di Rilevante Interesse Nazionale (PRIN) of the Italian Ministry of Research PHOTO (PHOtonics Terahertz devices based on tOpological materials) Grant No. 2020RPEPNH, and the European Union under Grant Agreement No. 101046424. Views and opinions expressed are however those of the author(s) only and do not necessarily reflect those of the European Union or the European Innovation Council. Neither the European Union nor the European Innovation Council can be held responsible for them.

The authors acknowledge fruitful discussions with Jens Biegert, Patrice Genevet, Michele Dipalo, Giovanni Melle, Sotirios Christodoulou, Anna Maria Cimini, and Domenico Bonanni.

## AUTHOR DECLARATIONS

### Conflict of Interest

The authors have no conflicts to disclose.

### Author Contributions

**Matteo Venturi**: Data curation (equal); Formal analysis (equal); Investigation (equal); Methodology (equal); Software (equal); Visualization (equal); Writing – original draft (equal); Writing – review & editing (equal). **Raju Adhikary**: Data curation (equal); Formal analysis (equal); Investigation (equal); Methodology (supporting); Software (supporting); Visualization (supporting); Writing – original draft (supporting); Writing – review & editing (equal). **Ambaresh Sahoo**: Data curation (supporting); Formal analysis (equal); Investigation (equal); Methodology (supporting); Software (supporting); Visualization (lead); Writing –original draft (supporting); Writing – review & editing (equal). **Carino Ferrante**: Investigation (supporting); Methodology (supporting); Project administration (supporting); Supervision (supporting); Visualization (supporting); Writing – original draft (supporting); Writing – review & editing (equal). **Isabella Daidone**: Formal analysis (supporting); Investigation (supporting); Methodology (supporting); Resources (supporting); Software (supporting); Supervision (supporting); Writing – original draft (supporting); Writing – review & editing (equal). **Francesco Di Stasio**: Conceptualization (supporting); Funding acquisition (equal); Project administration (supporting); Writing – review & editing (equal). **Andrea Toma**: Conceptualization (supporting); Funding acquisition (equal); Project administration (supporting); Writing – review & editing (equal). **Francesco Tani**: Conceptualization (supporting); Funding acquisition (equal); Project administration (supporting); Writing – review & editing (equal). **Hatice Altug**: Conceptualization (supporting); Funding acquisition (equal); Project administration (supporting); Writing – review & editing (equal). **Antonio Mecozzi**: Formal analysis (supporting); Investigation (supporting); Methodology (supporting); Writing – review & editing (equal). **Massimiliano Aschi**: Data curation (supporting); Formal analysis (supporting); Investigation (supporting); Methodology (equal); Resources (lead); Software (lead); Supervision (equal); Writing – original draft (supporting); Writing – review & editing (equal). **Andrea Marini**: Conceptualization (lead); Formal analysis (equal); Funding acquisition (equal); Investigation (equal); Methodology (equal); Project administration (equal); Software (equal); Supervision (equal); Visualization (equal); Writing – original draft (equal); Writing – review & editing (equal).

## DATA AVAILABILITY

The data that support the findings of this study are available within the article and its supplementary material.

## REFERENCES

*μ*m wavelength region