Effect of molecular concentration on excitonic nanostructure based refractive index sensing and near-field enhanced spectroscopy

Organic thin film based excitonic nanostructures are of a great interest in modern resonant nanophotonics as a promising alternative for plasmonic systems. Such nanostructures sustain propagating and localized surface exciton modes which can be exploited in refractive index sensing and near-field enhanced spectroscopy. To realize these surface excitonic modes and to enhance their optical performance, the concentration of the excitonic molecules present in the organic thin film has to be quite high so that a large oscillator strength can be achieved. Unfortunately, this often results in a broadening of the material response which might prevent achieving the very goal. Therefore, systematic and in-depth studies are needed on the molecular concentration dependence of the surface excitonic modes to acquire optimal performance from them. Here, we study the effect of molecular concentration in terms of oscillator strength and Lorentzian broadening on various surface excitonic modes when employed in sensing and spectroscopy. The optical performance of the modes is evaluated in terms of sensing, like sensitivity and figure of merit, as well as near-field enhancement, like


Introduction
Interaction of light with metallic nanostructures can excite a collective oscillation of the metal's conduction electrons, also known as plasmons.2][3] Depending on the type of the nanostructure, different plasmonic modes can be excited such as surface plasmon polariton (SPP) at the interface of a flat metal film and a dielectric material, 4 localized surface plasmon (LSP) in a metal nanoparticle (NP), 5 and plasmonic surface lattice resonance (PSLR) in a periodic structure, e.g., an array of metal NPs. 6asmonic modes are extremely sensitive to the dielectric constant of their surrounding medium and even a slightest change in the refractive index (RI) of the host medium can significantly shift the spectral position of the SPP, 7 LSP, 8 and PSLR 9 modes.9][10][11] Plasmonic modes (SPP, LSP, and PSLR) can also provide enhancement [12][13][14][15] and confinement [16][17][18] of light at the near-field close to the structure.Consequently, metallic nanostructures are widely exploited as resonant substrates for near-field enhanced spectroscopy ranging from weak [19][20][21][22] to strong [23][24][25] light-matter coupling.
6,27 The SPP mode can be supported by a flat metal film in the spectral region where Re{ϵ} < −1 while manifestation of LSP mode in a metal NP is only possible in the spectral regime where Re{ϵ} < −2. 27 the case of noble metals like gold and silver, the negative Re{ϵ} regime, i.e., the spectral regime where Re{ϵ} < −1 or −2, covers a major part of the visible spectrum, making them a popular choice in nanoplasmonics. 28,29spite the fact that plasmonic metarials show unique optical properties ranging from ultra-violet to infrared wavelengths, their performance is often hindered due to the absorption losses, and their fabrication might become too sophisticated to realize in a cost-effective way.Consequently, a quest emerges for alternative materials which can provide a plasmonlike negative Re{ϵ} regime, especially in the visible range, while exhibiting less losses as well as being somewhat simpler and inexpensive to fabricate compared to the metallic nanostructures.One important class of such materials is highly concentrated organic thin films possessing Frenkel excitons which induce a negative Re{ϵ} regime spectrally located very close to their strong excitonic absorbtion band. 26,27Such excitonic materials can support surface exciton polariton (SEP) at an interface of an excitonic film and a dielectric material, 26,27,30,31 localized surface exciton (LSE) in an excitonic NP, 27,32,33 and excitonic surface lattice resonance (ESLR) in a periodic array of excitonic NPs. 34The SEP, LSE, and ESLR modes are analogous to the SPP, LSP, and PSLR modes, respectively.Eventually, like the plasmonic modes, these surface excitonic modes show sensitivity towards the surrounding dielectric environment 31 and provide enhancement as well as confinement of the near-field. 35nce, excitonic nanostructures possesing these modes can be a potential alternative for the plasmonic systems in RI sensing and in near-field enhanced spectroscopy.
The optical responses associated with the aforementioned plasmonic and excitonic modes might appear analogous but the underlying physical mechanism in those systems differs fundamentally.The plasmonic resonances originate from the presence of free conduction electrons in metals which in the simplest case can be described by the Drude model.Con-trastingly, the excitonic modes in the organic thin fims appear due to the Frenkel excitons which can be expressed by the Lorentz oscillator model. 27Unlike Drude metals, the complex permittivity (ϵ) of an excitonic material is directly proportional to the Lorentz oscillator strength (f ) and the Lorentz linewidth (γ) of the material absorption 36,37 which scales with the molecular concentration. 27,32,33,38An increase in molecular concentration usually results in a rise in molecular absorption accompanied with a linewidth broadening, which accounts for a simultaneous rise in the magnitude of f and γ. 36,37 Such rise in f and γ can directly affect the magnitude of Re{ϵ} and thereby, the negative Re{ϵ} regime.As a consequence, the surface excitonic modes exhibit modification in their strength and light coupling efficiency. 26,27,39,40Therefore, optical performance of the surface excitonic modes can be tuned by varying the concentration of the excitonic molecules.
In this work, we investigate the effect of the molecular concentration (in terms of f and γ) on the performance of excitonic nanostructures when used for RI sensing and near-field enhanced spectroscopy.The J-aggregate of cyanine dye (TDBC) is considered as the excitonic molecule doped in a polyvinyl alcohol (PVA) matrix.Three kinds of excitonic nanostructures are studied, as shown in Figure 1 -(i) a TDBC-PVA thin film which supports SEP under excitation in the Kretschmann configuration (Figure 1a), (ii) a TDBC-PVA nanosphere which possesses LSE (Figure 1b), and (iii) a square lattice of TDBC-PVA nanospheres manifesting ESLR (Figure 1c).In all cases, the sensing performance is evaluated in terms of sensitivity and a commonly used figure of merit for RI sensing, i.e. the sensitivity divided by the width of the utilized spectral resonance, while the assessment in spectroscopy is based on near-field intensity enhancement (NFIE) and field-confinement.Our numerical findings show that the performance parameters (sensitivity, figure of merit, NFIE, field-confinement) of a surface excitonic mode can be tuned efficiently by varying the molecular concentration.Moreover, SEP, LSE, and ESLR based nanostructures provide different degrees of tunability when concentration is varied.Our comprehensive study on different types of surface excitonic modes with varying concentration provides key information for developing and optimizing novel organic material based excitonic nanodevices for sensing and spectroscopy.

Negative Re{ϵ} regime
Before analyzing the performance of different excitonic systems it is important to determine their negative Re{ϵ} regime, i.e., the spectral regime where Re{ϵ} < −1 or −2, as a function of Lorentz oscillator strength (f ) and Lorentz linewidth (γ).The complex and dispersive dielectric function (ϵ) of a TDBC-PVA system can be estimated using the Lorentz oscillator model (LOM) 27,37,41 as where E is the energy, ϵ ∞ is the dielectric constant of the host polymer (i.e.PVA), f is the oscillator strength of the excitonic absorption having E 0 as its spectral peak position and γ as its spectral linewidth. 27,37,41In our computation, we consider ϵ ∞ = 2.1025 and E 0 = 2.08 eV to have a realistic values to start with and to be able to compare with the existing literature 41 while f and γ are treated as variables.
An increase in molecular concentration results in an increase in molecular absorption usually accompanied with a linewidth broadening accounting for a simultaneous rise in f and γ. 36,37 To model that we calculate real (Re{ϵ}) and imaginary (Im{ϵ}) parts of the dielectric function (ϵ) of a 60 nm thick TDBC-PVA layer using eq 1 with varying f and γ.The curves are shown in Figure 2a.The associated absorption is calculated using transfer-matrix method (TMM) 42,43 implemented in MATLAB, 44,45 similarly as in our earlier studies.The green curves in Figure 2a represent Re{ϵ} (solid) and Im{ϵ} (dashed) of our pristine TDBC-PVA film with f = 0.05 and γ = 0.05 eV.The corresponding absorption is shown in the inset of Figure 2a (green curve).It is clear from the figure that our pristine layer is unable to support any surface excitonic mode since its Re{ϵ} is positive in the wavelength region of interest (500-700 nm).To address a rise in concentration, we first increase f to 0.20 while keeping γ at 0.05 eV.The red curves in Figure 2a depict the case with the corresponding absorption with the same color in the inset.Clearly now Re{ϵ} becomes negative (almost −2) indicating that our TDBC layer can support the surface excitonic modes in a narrow spectral window (∼ 575 -595 nm) at the blue side of the molecular absorption peak (∼ 600 nm).However, to realize the actual effect of a rising concentration one should increase both f and γ simultaneously.The blue curves in Figure 2a show the case (with the related absorption in the inset) where f is kept at 0.20 and γ rises from 0.05 eV to 0.15 eV.Clearly, the increase in γ counteracts the effect seen for the sole rise in only f by making Re{ϵ} positive again like in the pristine case, and eventually, no surface excitonic mode can be supported by the TDBC layer.
To develop more insight on this counteracting behaviour we calculate the spectral regions where Re{ϵ} < −1 and Re{ϵ} < −2, reported in Figure S1 in Supporting Information (SI), for different values of f and γ.In our spectral region selection, we impose also an additional condition, i.e., |Im{ϵ}| < |Re{ϵ}| to ensure minimal material loss. 40The bandwidth (BW) of the surface excitonic modes is evaluated as the difference between the upper and the lower boundaries of the aforementioned spectral regions (see Figure S1 in SI).The solid curves in Figure 2b report the BW of SEP mode (Re{ϵ} < −1) while the dashed curves report the same for LSE and ESLR mode (Re{ϵ} < −2).
In Figure 2b, at γ = 0.05 eV, the vertical axis presents the scenario where the BW is increasing with increasing f , i.e., f = 0.40 (green) to f = 0.75 (red) via f = 0.50 (blue), considering a constant γ (no broadening).However, when the broadening is incorporated, i.e., γ increases from 0.05 eV to 0.20 eV for a constant value of f (0.40 or 0.50 or 0.75), in all cases, the BW drops drastically and vanishes after a certain value of γ as one can see in Figure 2b.This finding clearly indicates that when both f and γ increase due to a rise in concentration, they counteract each other's effects.
Interestingly, the range of γ in which the BW is non-zero (e.g., up to 0.14 eV for the dashed red curve) differs for different magnitudes of f as one can see in Figure 2b.This range (i.e., 0.14 eV for the dashed red curve) can be considered as a broadening tolerance (∆γ) of a surface excitonic mode since at any broadening lower than ∆γ the mode exists at certain spectral region.However, if the broadening is higher than ∆γ, the BW of the suitable spectral region vanishes so as the surface excitonic mode.The evolution of ∆γ as a function of f is plotted in the inset of Figure 2b and it is clear from the figure that the higher the f , the larger the ∆γ.This is an important finding since it can provide a solution to mitigate the above-mentioned counteracting problem.By choosing a relatively high concentration of molecules one can increase f which will push the value of Re{ϵ} well below zero at the blue side of the molecular absorption peak and increase the magnitude of ∆γ to tolerate the inevitable linewidth broadening.Consequently, the system will better sustain the surface excitonic mode.

Surface exciton polariton
After establishing the initial conditions as well as the spectral range where TDBC-PVA system can support the surface excitonic modes, we first focus on SEP mode under the Kretschmann configuration. 30,31The SEP mode can be excited in a multilayer system such as air/TDBC-PVA thin film/prism structure where the p-polarized incident light is coupled through the prism.The air can be replaced by the sensing medium for sensing application 31 and by the analyte for spectroscopy. 23,36The schematic of such SEP based system is presented in Figure 1a.We use the Fresnel multilayer reflection theory 7,46,47 implemented in MATLAB for calculating the reflectivity (R) of the system since SEP mode is manifested as a dip in the attenuated total reflection (ATR) spectrum. 47The RI of the prism (n p ) is considered as 1.50 which corresponds to the common BK7 glass in practice. 7The RI of the sensing medium (n s ) is varied from 1 to 1.01 with a step size of 0.001 to evaluate the performance of the sensor.The RI of the TDBC-PVA film is obtained as n e = √ ϵ, 48 where ϵ is calculated using eq 1.
We excite the SEP mode supported by a 60 nm thick TDBC-PVA film (f = 0.5 and γ = 0.05 eV) using the Kretschmann configuration in two ways.In the angular scheme we use the p-polarized monochromatic light of wavelength λ ex to excite the system over a broad range of incident angles higher than the critical angle of total internal reflection (∼ 42 The angle-dependent reflectivity is presented in Figure 3a (blue curve) for λ ex = 569 nm.
The dip found in the reflection profile is the signature of the excited SEP mode.In the spectral scheme, we excite the system by a broadband source (p-polarized white light) at a fixed incident angle (θ ex ) and the reflectivity is computed over a wide spectral range.The wavelength-dependent reflectivity is depicted in Figure 3a (red curve) for θ ex = 54 • .Similar to the angular case, profound presence of the SEP mode is found as a dip in the spectral reflectance.
To obtain the optimal excitation conditions (i.e.θ ex and λ ex ) of the SEP mode, we compute the reflectance R(θ ex , λ ex ), with all the angles (42 • − 90 • ) and wavelengths supporting the SEP, i.e., within the BW discussed in previous section.The results are reported as a contour map in Figure 3b.In the figure, the white dashed curve shows the dispersion of the SEP mode following the spectral and angular minima of the reflectance.The optimal excitation angle (θ ex ) and wavelength (λ ex ) for sensing are evaluated as the position where R(θ ex , λ ex ) is the minimum of the whole contour map as shown by the black dotted lines in Figure 3b.
The excitation conditions can also vary with respect to f and γ since the BW of the SEP mode is concentration-dependent.To address this, we compute the dispersion of the SEP mode for different f and γ.To study the effect of f , it is varied from 0.30 to 0.90 (for f < 0.3 BW≈ 0) with a step size of 0.05 while keeping γ = 0.05 eV (no broadening).To study the effect of broadening, γ is varied from 0.05 eV to 0.09 eV (extent of ∆γ) with a step size of 0.01 eV while keeping f = 0.5 constant.In both cases, we extract the excitation conditions The evolution of the excitation wavelength (λ ex ) as a function of f (when γ = 0.05 eV) and of γ (when f = 0.5) is illustrated in Figure 3c.From the figure it is clear that λ ex is significantly blue-shifted with increasing f when no broadening is allowed (red curve in Figure 3c).This is consistent with our finding in Figure S1 (see SI) where the BW of SEP mode widens only in the blue-wavelength side with increasing f .However, when the broadening is introduced, λ ex experiences a mild red-shift (blue curve in Figure 3c) counteracting the effect of sole rise only in f without broadening.
On the other hand, the angle of excitation (θ ex ) is almost unaffected (≈ 54 • ) irrespective of whether f or γ is varied (not shown).
Therefore, for each f (when γ = 0.05 eV) or for each γ (when f = 0.5) there will be a corresponding λ ex at which the SEP mode can be optimally excited over a broad range of incident angles in the angular scheme.On the other hand, at θ ex ≈ 54 • the SEP mode can be optimally excited over a wide range of wavelengths in the spectral scheme irrespective of the magnitude of f and γ.Furthermore, one can tune the spectral region of excitation (λ ex ) by varying f and γ.
The near-field intensity enhancement (NFIE) is a crucial parameter for surface-enhanced spectroscopy and can be calculated as |E| 2 where E = E loc /E 0 represents the enhanced (electric) near-field (E loc ) normalized by the incident field (E 0 ). 13,18We perform finite-difference time-domain (FDTD) 49,50 simulation to calculate the spatial near-field intensity profile of |E| 2 for the SEP mode shown in Figure 3d.Like SPP, the evanescent nature of the SEP mode can be seen from the figure and it is consistent with the earlier findings. 31,40e performance of a RI sensor can be quantified in terms of its sensitivity (S) and figure of merit (F ).In the angular domain, the angular sensitivity (S θ ) of a SEP sensor can be defined as where ∆θ dip represents the shift in the angular position of the reflectance dip (θ dip ) due to a change in RI (∆n s ) of the sensing medium (n s ).The angular figure of merit (F θ ) is expressed as with ∆θ as the angular full-width at half-maximum (FWHM) of the SEP mode at n s = 1 (air).Similarly, in the spectral domain, the spectral sensitivity (S λ ) of a SEP sensor can be formulated as where ∆λ dip represents the shift in the spectral position of the reflectance dip (λ dip ) due to a change in RI (∆n s ) of the sensing medium (n s ).The spectral figure of merit (F λ ) is then with ∆λ as the spectral full-width at half-maximum (FWHM) of the SEP mode at n s = 1 (air). 7,9,31In practice, the sensitivities (S θ and S λ ) are calculated as a slope of the calibration curve, i.e., a plot of the reflectance minimum (θ dip in deg and λ dip in nm) as a function of the RI of sensing medium (n s in refractive index unit or RIU).The slope is extracted from a linear fit on the calibration curve (see Figure S2a in SI).
The effect of f and γ on the sensing performance of a SEP-based system can be understood from Figure 4.In Figure 4a, the angular sensitivity (S θ ) and figure of merit (F θ ) are plotted as a function of f when no broadening is considered (γ = 0.05 eV).From the figure it is clear that both S θ and F θ increase with increasing f .Similar trend is found in spectral sensitivity (S λ ) and figure of merit (F λ ) as one can see in Figure 4c.Along with a rise in both sensitivities (S θ and S λ ), the FWHM of the SEP mode experiences a narrowing in both angular (∆θ) and spectral (∆λ) domains due to a sole rise in f only (see Figure S2c in SI) which results in a monotonic increase in the figure of merits (F θ and F λ ).
Incorporation of broadening, i.e., increasing γ within ∆γ while keeping f = 0.5, results in a drastic drop in S θ and a mild fall in S λ as one can see in Figures 4b and 4d.Moreover, both ) and Purcell enhancement (Φ P ) as a function of (e) f and (f) γ; field-confinement (Φ C ) as a function of (g) f and (h) γ.In the figures in left panel, f is varied when γ = 0.05 eV.In the figures in right panel, γ is varied within ∆γ when f = 0.5.In figures (a)-(f), the blue and red vertical axes correspond to the blue and red curves, respectively.In all figures, the blue circles, red squares, and black triangles connected by the curves of corresponding color depict the discrete data points.∆θ and ∆λ increase when the broadening is considered (see Figure S2d in SI).As a result, both F θ and F λ drop with a sole rise in γ only.Such outcome implies that the performance of a SEP sensor can be tuned by varying its molecular concentration and the broadening counteracts the positive effect of increasing f .The performance of our SEP-based system as a resonant platform for near-field enhanced spectroscopy can be determined in terms of NFIE (|E| 2 ), Purcell enhancement, and fieldconfinement.The NFIE is directly proportional to the electromagnetic enhancement utilized in surface-enhanced spectroscopy. 13,18The Purcell enhancement for a weak light-matter coupling is the amount of emission enhancement, which is determined by the ratio between the temporal and the spatial confinement of light field. 51The temporal confinement is defined by the quality factor (Q) while the spatial confinement is determined by the mode volume (V m ), and thus the whole Purcell enhancement is Φ P ∝ Q/V m . 51,52The field-confinement is expressed as , which is directly proportional to the coupling strength in a single-molecular picture, when the light-matter interaction is strong. 17,53e effect of f and γ on |E| 2 , Φ P , and Φ C can be seen in Figures 4e to 4h The Purcell enhancement (Φ P ) and field-confinement (Φ C ) improve when Q increases along with a drop in V m .That happens for increasing f when γ = 0.05 eV is constant (see Figure S2e in SI).Consequently, Φ P and Φ C show a monotonic increase as a function of f as shown in Figures 4e and 4g.In the presence of broadening (at f = 0.5), however, Q decreases accompanied with a rise in V m (see Figure S2f in SI).Eventually, Φ P and Φ C drop with an increase in γ as depicted in Figures 4f and 4h.We can infer from such outcomes that efficiency of the SEP mode in confining and enhancing the near-field can be optimized by varying the molecular concentration and like sensing, here also the broadening acts against the positive effect of increasing f .

Localized surface exciton
After showing that the SEP mode can be exploited for sensing and spectroscopy, and its efficiency can be tuned by the molecular concentration, we next investigate the localized surface exciton (LSE) based system, i.e., a TDBC-PVA nanosphere illustrated in Figure 1b.
The radius (r) of the nanosphere is taken as 50 nm and the RI of the TDBC-PVA material (n e ) is obtained as n e = √ ϵ, 48 where ϵ is calculated using eq 1.The RI of the sensing medium (n s ) is varied again from 1 to 1.01 with a step size of 0.001 to evaluate the performance of the sensor.
The LSE mode of an excitonic NP manifests as a broad peak in its extinction spectrum. 27,32,33We employ Mie theory [55][56][57][58][59] implemented in MATLAB to compute the extinction efficiency, i.e., the extinction cross-section normalized by the geometrical cross-section, of the nanosphere since its size (2r = 100 nm) is beyond the quasi-static limit. 60In our calculation, the NP is excited by normal incidence of light.
The simulated extinction efficiency (Q ext ) in air for the nanosphere with f = 0.5 and γ = 0.05 eV is reported in Figure 5a where the LSE mode is profound as a broad peak around 569 nm.The spatial distribution of NFIE at that wavelength computed by the FDTD method is shown in Figure 5b which resembles a dipolar resonance identical to the particle plasmon mode. 61The spectral sensitivity (S λ ) and figure of merit (F λ ) of the excitonic nanosphere are calculated using eq 4 and eq 5, respectively, where ∆λ is the FWHM of the LSE mode at n s = 1 (air) and λ dip is replaced by the spectral peak position of the LSE mode (λ peak ).
We track λ peak (≈ 569 nm) as a function of n s to construct the calibration curve.Then, S λ is determined as the slope of that curve through a linear fit similar to the case of SEP. ) and Purcell enhancement (Φ P ) as a function of (e) f and (f) γ; field-confinement (Φ C ) as a function of (g) f and (h) γ.In the left panel of figures (c)-(h), f is varied when γ = 0.05 eV while in the right panel, γ is varied within ∆γ when f = 0.5.The blue circles, red squares, and black triangles connected by the curves of corresponding color depict the calculated discrete data points.In figures (c)-(f), the blue and red vertical axes correspond to the blue and red curves, respectively.The f -dependent profiles of the sensing parameters (S λ and F λ ) are plotted in Figure 5c when no broadening is allowed (γ = 0.05 eV).From the figure it is clear that both S λ and F λ monotonically increase with a rise in f , similar to the trend found in the case of SEP.
Incorporation of broadening, i.e., varying γ within ∆γ while f = 0.5, shows almost no effect on S λ , however, F λ drops significantly due to a rise in ∆λ (see Figure S3 in SI), as one can see in Figure 5d.
The f -and γ-dependent profiles of |E| 2 , Φ P , and Φ C for the LSE mode can be seen from Figures 5e to 5h.From the figures it is clear that similar to SEP, |E| 2 max and Φ C increase with rise in f only (γ = 0.05 eV) while drop when the broadening is incorporated (at f = 0.5).Identical trend is found for |E| 2 avg while the trend is opposite for V m (see Figure S3 in SI) which explains the profile of Φ C .Strikingly, the trend of Φ P is monotonically decreasing irrespective of the broadening.That is because, unlike in SEP, ∆λ of the LSE mode increases and hence, Q drops regardless of whether f or γ is increasing (see Figure S3 in SI).Based on these findings, we can reckon that like SEP, the performance of the LSE mode in sensing and spectroscopy can also be modified via molecular concentration where the effects of f and γ are mostly counteracting.

Excitonic surface lattice resonance
After confirming that both the fundamental surface excitonic modes of the excitonic material are promising as a RI sensor and resonant substrate, we delve into a periodic array of previous NPs possessing excitonic surface lattice resonance (ESLR).The ESLR mode is usually much sharper/narrower and stronger than the dipolar LSE mode present in an isolated NP. 9 To advance this idea, we study a two-dimensional (2D) array (square lattice) of excitonic nanospheres having a well-defined lattice period (D) in both x and y directions as illustrated in Figure 1c.
The ESLR mode performs optimally when the mediums above and below the array have identical RI. 9,62 Keeping that in mind we consider that our designed array is in an index-matched environment having the same RI (n s ) everywhere.In practice, it can be implemented by having the array on a glass substrate with an index-matching oil on top. 9,62e sensing performance of the array is evaluated by varying n s similar to the case of SEP and LSE.
The ESLR mode of a NP array manifests as a sharp peak in the extinction spectrum of the array.Such mode can only be excited when the Rayleigh anomaly (or diffraction edge) of the array exists at a higher wavelength than the LSE mode of the individual NPs present in that array. 9The lattice period (D) of our array is considered as D = 400 nm yielding the Rayleigh anomaly around 600 nm which is at a longer wavelength compared to the LSE mode of our individual nanosphere (569 nm).The number of nanospheres (N ) included in the array is taken as N = 400 resulting in a square lattice of N × N nanospheres.The extinction profile of our NP array is computed using the coupled dipole (CD) method 34,[63][64][65][66][67][68][69][70] implemented in MATLAB.In our computation, the array is excited by normal incidence of light and the nanospheres present in the array are identical with the one discussed in the previous section.
The simulated extinction efficiency (Q ext ) of the array is reported in Figure 6a for f = 0.5 and γ = 0.05 eV.The sharp ESLR mode is profound at a wavelength of 606 nm, i.e., higher than the Rayleigh anomaly (600 nm) shown by the dashed vertical line.The spatial distribution of NFIE around each particle at the ESLR wavelength computed by the FDTD method is shown in Figure 6b.It clearly depicts a stronger dipole like resonance compared to that of the LSE mode.
The sensing behaviour of our NP array can be understood from Figures 6c and 6d where the sensing parameters (S λ and F λ ) are evaluated using the similar approach employed for the LSE mode.Interestingly, from the figures, one can see that unlike SEP and LSE, S λ of the ESLR mode increases with both increasing f and γ.However, in both cases, F λ drops noticeably.That is because, like in LSE, here also ∆λ of the ESLR mode increases along ) and Purcell enhancement (Φ P ) as a function of (e) f and (f) γ; field-confinement (Φ C ) as a function of (g) f and (h) γ.In the left panel of figures (c)-(h), f is varied when γ = 0.05 eV while in the right panel, γ is varied within ∆γ when f = 0.5.The blue circles, red squares, and black triangles connected by the curves of corresponding color depict the calculated discrete data points.In figures (c)-(f), the blue and red vertical axes correspond to the blue and red curves, respectively.with a drop in Q regardless of whether f or γ is increasing (see Figure S4 in SI).
The f -and γ-dependent profiles of |E| 2 max are reported in Figures 6e and 6f, respectively.
The figures show an increase in |E| 2 max with a sole rise in f only (γ = 0.05 eV) while a drop when the broadening is incorporated (at f = 0.5).The trend is same for |E| 2 avg (see Figure

Comparision with gold
To compare our excitonic systems with their plasmonic analogs, we study similar gold (Au) nanostructures (Au thin film, Au nanosphere and its 2D array) in identical numerical environment where the material model for Au is taken from existing literature. 71A detailed comparison in tabular form can be found in Table S1 (see SI).
Succinctly, we found that the SEP mode performs comparable or better in angular RI sensing compared to the SPP mode which is consistent with the earlier finding. 31The LSE mode provides comparable or better electromagnetic enhancement for surface-enhanced spectroscopy than that of the LSP mode which is also inline with the existing literature. 35However, the most surprising and important finding that all the surface excitonic (SEP, LSE, and ESLR) provide Q and lower V m resulting in better (or comparable) Purcell enhancement (Φ P ) and field confinement (Φ C ) compared to their plasmonic counterparts.
Such outcomes strongly validate the fact that excitonic nanostructures are a potential alternative for plasmonic systems in RI sensing and enhanced spectroscopy.

Conclusion
Concisely, we investigated effect of molecular concentration on excitonic nanostructure based refractive index sensing and near-field enhancement suitable for surface enhanced spectroscopy.Three kinds of excitonic nanostructures were considered -a TDBC-PVA thin film supporting surface exciton polariton (SEP), a TDBC-PVA nanosphere possessing localized surface exciton (LSE), and a square lattice of similar nanospheres manifesting excitonic surface lattice resonance (ESLR).The effect of molecular concentration was studied by varying oscillator strength (f ) and the Lorentzian broadening (γ) of the TDBC-PVA material.
The performance in sensing and spectroscopy was evaluated in terms of sensitivity, figure of merit, near-field intensity enhancement, Purcell enhancement, and field confinement.Our numerical findings revealed that most of the performance parameters showed a rise in their values when the oscillator strength was increased without any additional Lorentzian broadening.However, when the broadening was considered, the parameter values dropped implying a counteracting effect.Such outcome indicates that one can tune the optical performance of an excitonic system through its molecular concentration which is not possible in typical plasmonic systems.Moreover, different surface excitonic modes showed different degrees of tunability and equivalency in performance when compared to gold.
In line with our results on various excitonic systems, we can infer that to achieve an efficient performance from these systems, one should aim a molecular concentration corresponds to a large value of f .In practice, however, this approach might incur formation of molecular aggregates at extremely high concentration and thereby, induces challenge to maintain a relatively small value for γ within the broadening tolerance.Such limitation can be mitigated by selecting a molecule possessing strong transition dipole moment with narrow spectral linewidth since then a large f can be achieved with comparatively low molecular concentration while maintaining a small value of γ.Therefore, we can conclude that excitonic systems offer an extra degree of tunability via molecular concentration and are a promising alternative for plasmonics.Our comprehensive study provides key information to Average near-field intensity enhancement (|E| 2 avg ) and spectral full width at half maximum (FWHM) (∆λ) as a function of (a) oscillator strength (f ), and (b) Lorentz linewidth (γ).The quality factor (Q) and mode volume (V m ) as a function of (c) f , and (d) γ.In all cases, f is varied with γ = 0.05 eV and γ is varied with f = 0.5.In all figures, the blue and red vertical axes correspond to the blue and red curves, respectively, while the blue circles and the red squares on the curves of corresponding color depict the discrete data points. .Properties of the excitonic surface lattice resonance (ESLR) mode of a 400×400 square lattice of 100 nm TDBC-PVA nanospheres with a lattice period of 400 nm.Average near-field intensity enhancement (|E| 2 avg ) and spectral full width at half maximum (FWHM) (∆λ) as a function of (a) oscillator strength (f ), and (b) Lorentz linewidth (γ).The quality factor (Q) and mode volume (V m ) as a function of (c) f , and (d) γ.In all cases, f is varied with γ = 0.05 eV and γ is varied with f = 0.5.In all figures, the blue and red vertical axes correspond to the blue and red curves, respectively, while the blue circles and the red squares on the curves of corresponding color depict the discrete data points.

Figure 2 :
Figure 2: (a) The real (Re{ϵ}, solid curves) and imaginary (Im{ϵ}, dashed curves) parts of the dielectric function (ϵ) of a 60 nm thick TDBC-PVA layer calculated using eq 1 for different values of Lorentz oscillator strength (f ) and Lorentz linewidth (γ).Here, ϵ ∞ = 2.1025 and E 0 = 2.08 eV as discussed in the text.The corresponding absorption spectra (in matching colors) computed by TMM are shown in the inset.The green spot on the figure depicts the region where Re{ϵ} < 0 and |Im{ϵ}| < |Re{ϵ}| for the red curves.(b) Bandwidth (BW) of surface excitonic modes for different values of f and γ.In the inset, the broadening tolerance (∆γ) is plotted as a function of f .

Figure 3 :
Figure 3: (a) Angular (excited at λ ex = 569 nm) and spectral (excited at θ ex = 54 • ) reflectance of a 60 nm thick TDBC-PVA film (f = 0.5 and γ = 0.05 eV) under Kretschmann configuration.(b) Reflectance of the same film as a contour map where the white dashed curve shows the dispersion of the SEP mode and the black dotted lines show the optimal excitation conditions with minimal reflectance R(θ ex , λ ex ).(c) Evolution of the optimal excitation wavelength (λ ex ) as a function of f and γ.The value of f is varied when γ = 0.05 eV and the value of γ is varied when f = 0.5.(d) FDTD simulated near-field intensity profile of SEP mode.In (a) and (c), the blue and red horizontal axes correspond to the blue and red curves, respectively, while in (c), the blue circles and red squares on the curves of corresponding color depict the discrete data points.

Figure 4 :
Figure 4: Performance parameters of the SEP mode supported by a 60 nm thick TDBC-PVA film under the Kretschmann configuration -angular sensitivity (S θ ) and figure of merit (F θ ) as a function of (a) f and (b) γ; spectral sensitivity (S λ ) and figure of merit (F λ ) as a function of (c) f and (d) γ; NFIE maximum (|E| 2max ) and Purcell enhancement (Φ P ) as a function of (e) f and (f) γ; field-confinement (Φ C ) as a function of (g) f and (h) γ.In the figures in left panel, f is varied when γ = 0.05 eV.In the figures in right panel, γ is varied within ∆γ when f = 0.5.In figures (a)-(f), the blue and red vertical axes correspond to the blue and red curves, respectively.In all figures, the blue circles, red squares, and black triangles connected by the curves of corresponding color depict the discrete data points.

Figure 5 :
Figure 5: (a) Extinction efficiency (Q ext ) of a TDBC-PVA nanosphere having a diameter of 100 nm, f = 0.5, and γ = 0.05 eV.(b) Spatial distribution of NFIE around the nanosphere in air at its LSE resonance wavelength 569 nm computed by FDTD method.Performance parameters of the LSE mode -spectral sensitivity (S λ ) and figure of merit (F λ ) as a function of (c) f and (d) γ; NFIE maximum (|E| 2max ) and Purcell enhancement (Φ P ) as a function of (e) f and (f) γ; field-confinement (Φ C ) as a function of (g) f and (h) γ.In the left panel of figures (c)-(h), f is varied when γ = 0.05 eV while in the right panel, γ is varied within ∆γ when f = 0.5.The blue circles, red squares, and black triangles connected by the curves of corresponding color depict the calculated discrete data points.In figures (c)-(f), the blue and red vertical axes correspond to the blue and red curves, respectively.

Figure 6 :
Figure 6: (a) Extinction efficiency (Q ext ) of a 400 × 400 square lattice of TDBC-PVA nanospheres having a diameter of 100 nm and a lattice period of 400 nm with f = 0.5 and γ = 0.05 eV.The vertical dashed line represents the spectral position of the Rayleigh anomaly.(b) Spatial distribution of NFIE around a single particle computed by FDTD method at the wavelength of ESLR.Performance parameters of the ESLR -spectral sensitivity (S λ ) and figure of merit (F λ ) as a function of (c) f and (d) γ; NFIE maximum (|E| 2max ) and Purcell enhancement (Φ P ) as a function of (e) f and (f) γ; field-confinement (Φ C ) as a function of (g) f and (h) γ.In the left panel of figures (c)-(h), f is varied when γ = 0.05 eV while in the right panel, γ is varied within ∆γ when f = 0.5.The blue circles, red squares, and black triangles connected by the curves of corresponding color depict the calculated discrete data points.In figures (c)-(f), the blue and red vertical axes correspond to the blue and red curves, respectively.
Figure S4 in SI).Despite that fact, Φ P shows a decreasing nature due to the same trend in Q as mentioned before irrespective of the broadening.Such findings confirm the dependency of the ESLR mode on molecular concentration and thereby, its tunibility considering the counteracting effects of f and γ.

Figure S3 .
Figure S3.Properties of the localized surface exciton (LSE) mode of a 100 nm TDBC-PVA nanosphere.Average near-field intensity enhancement (|E| 2 avg ) and spectral full width at half maximum (FWHM) (∆λ) as a function of (a) oscillator strength (f ), and (b) Lorentz linewidth (γ).The quality factor (Q) and mode volume (V m ) as a function of (c) f , and (d) γ.In all cases, f is varied with γ = 0.05 eV and γ is varied with f = 0.5.In all figures, the blue and red vertical axes correspond to the blue and red curves, respectively, while the blue circles and the red squares on the curves of corresponding color depict the discrete data points.
Figure S4.Properties of the excitonic surface lattice resonance (ESLR) mode of a 400×400 square lattice of 100 nm TDBC-PVA nanospheres with a lattice period of 400 nm.Average near-field intensity enhancement (|E| 2 avg ) and spectral full width at half maximum (FWHM) (∆λ) as a function of (a) oscillator strength (f ), and (b) Lorentz linewidth (γ).The quality factor (Q) and mode volume (V m ) as a function of (c) f , and (d) γ.In all cases, f is varied with γ = 0.05 eV and γ is varied with f = 0.5.In all figures, the blue and red vertical axes correspond to the blue and red curves, respectively, while the blue circles and the red squares on the curves of corresponding color depict the discrete data points.