Enhancement of dynamic sensitivity of multiple surface-plasmonic-polaritonic sensor using silver nanoparticles
Farhat Abbas, Muhammad Faryad, Stephen E. Swiontek, Akhlesh Lakhtakia
aa r X i v : . [ phy s i c s . op ti c s ] S e p Enhancement of dynamic sensitivity of multiplesurface-plasmonic-polaritonic sensor using silvernanoparticles
Farhat Abbas, Muhammad FaryadDepartment of Physics, Lahore University of Management Sciences,Lahore, 54792, Pakistan. Email: [email protected] E. Swiontek, Akhlesh LakhtakiaDepartment of Engineering Science and Mechanics, PennsylvaniaState University, University Park, Pennsylvania 16802, USA.Email: [email protected] 11, 2018
Abstract
Multiple surface plasmon-polariton (SPP) waves excited at the inter-face of a homogeneous isotropic metal and a chiral sculptured thin film(STF) impregnated with silver nanoparticles were theoretically assessedfor the multiple-SPP-waves-based sensing of a fluid uniformly infiltratingthe chiral STF. The Bruggemann homogenization formalism was used intwo different modalities to determine the three principal relative permit-tivity scalars of the silver-nanoparticle-impregnated chiral STF infiltrateduniformly by the fluid. The dynamic sensitivity increased when silvernanoparticles were present, provided their volume fraction did not exceedabout 1%.
Optical sensors that rely on the variability of the excitation of a surface plasmon-polariton (SPP) wave guided by the planar interface of a metal and a homoge-neous isotropic dielectric (HID) material with respect to the refractive index ofthe latter material are widely used to detect and quantify the concentrations ofanalytes [1, 2, 3]. At any given free-space wavelength λ , only one SPP wavecan be excited in a sensor of this kind [4] and can be used to detect a singleanalyte present in the HID material [2, 3].Despite successes, strategies to economically [5] improve reliability continueto be devised. One strategy is to disperse a small volume fraction of metal1anoparticles in the HID material [6, 7, 8], which is usually a fluid for sens-ing applications. This strategy exploits the excitation of the Fr¨ohlich mode[9] or a localized surface-plasmon resonance [10] in a metal nanoparticle by anSPP wave. Metal nanoparticles have been reported to increase the sensitivity,depending on the substrate as well as the shape and material of the nanopar-ticles [6, 7, 11, 12]. Also, metal nanoparticles are necessary to provide sites forrecognition molecules that would bind to the specific analyte to be detected [13].An emerging strategy is to replace the HID material by a periodically nonho-mogeneous dielectric (PHD) material that is porous [14]. The planar interfaceof a metal and a PHD material is capable of guiding multiple SPP waves ofthe same frequency and direction of propagation but with different polarizationstates, phase speeds, spatial profiles, attenuation rates, and degrees of localiza-tion to the interface [15]. If the PHD material is porous, it can be infiltratedwith the analyte to be sensed. Multiple SPP waves provide the opportunity formore reliable and more sensitive optical sensing than a single SPP wave. Thishas been established both theoretically and experimentally using sculpturedthin films (STFs) as porous PHD materials [14, 16, 17]. However, the effect ofinfiltration of the STF by metal nanoparticles in a multiple-SPP-waves-basedsensing scenario is not known.Therefore, we set out to investigate multiple-SPP-waves-based sensing inwhich a chiral STF [18] is infiltrated by metal nanoparticles as well as a fluid. Achiral STF is an ensemble of parallel nanohelixes, and is therefore macroscopi-cally conceptualized as an anisotropic and helically nonhomogeneous material inthe optical spectral regime. We first determined the complex wavenumbers q ofSPP waves in a canonical boundary-value problem in which a metal and a chiralSTF occupy adjoining half spaces. Then we determined the angle of incidence θ inc of light that is needed to excite an SPP wave in the Turbadar–Kretschmann–Raether prism-coupled configuration [15] employed for experiments.The plan of this paper is as follows: Sec. 2.1 describes the calculation ofthree nanoscale parameters by using the inverse Bruggeman homogenizationformalism and the use of the forward Bruggeman homogenization formalismto determine the constitutive parameters of the chiral STF [16] in which silvernanoparticles are placed and whose void regions are in infiltrated by a fluid.In Sec. 3, numerical results of the canonical boundary-value problem and theprism-coupled configuration are presented and discussed. Concluding remarksare presented in Sec. 4. An exp( − iωt ) dependence on time t is implicit, where ω is the angular frequency and i = √−
1. The Cartesian unit vectors are denotedby ˆ u x , ˆ u y , and ˆ u z ; dyadics are double underlined; vectors are in bold face; andthe free-space wavenumber and wavelength are denoted by k = ω √ ε µ and λ = 2 π/k , respectively, where µ is the permeability of free space and ε is thepermittivity of free space. 2 Theory in Brief
Chiral STFs are usually fabricated using physical vapor deposition by directinga vapor flux towards a rotating substrate at an angle χ v [18]. The angle χ v , thedeposition rate, and the rotation speed of the substrate are the main factors onwhich the porosity of the chiral STF depends. The relative permittivity dyadicof a chiral STF is stated as ε Chi ST F ( z ) = S z ( z ) · S y ( χ ) · ε ◦ ref · S − y ( χ ) · S − z ( z ) , (1)with the dyadics S z ( z ) = ˆ u z ˆ u z + (ˆ u x ˆ u x + ˆ u y ˆ u y ) cos( hπz/ Ω)+ (ˆ u y ˆ u x − ˆ u x ˆ u y ) sin( hπz/ Ω) S y ( χ ) = ˆ u y ˆ u y + (ˆ u x ˆ u x + ˆ u z ˆ u z ) cos χ + (ˆ u z ˆ u x − ˆ u x ˆ u z ) sin χε ◦ ref = ε a ˆ u z ˆ u z + ε b ˆ u x ˆ u x + ε c ˆ u y ˆ u y ; (2)where the direction of helical nonhomogeneity is parallel to the z axis, χ ∈ (0 , π/
2] is the angle of rise of the nanohelixes in the chiral STF with respectto the xy plane, 2Ω is the helical period, and h = +1 for structural righthandedness but h = − ε a , ε b , and ε c will be differ-ent for an as-deposited chiral STF than for a chiral STF containing the metalnanoparticles and/or infiltrated by a fluid. The process to determine these quan-tities for the present work relies on both experimental data and a theoreticalmicroscopic-to-continuum model [16]. The as-deposited chiral STF is supposedto be made of a material of refractive index n s , this material assumed to bedeposited in the form of electrically small ellipsoids with a transverse aspectratio γ b somewhat larger than unity and a slenderness ratio γ τ ≫
1; i.e., ev-ery nanohelix is a string of ellipsoidal sausages. The volume fraction of thedeposited material is denoted by f s ∈ [0 , n np . The fluidis taken to be distributed as electrically small spheres of refractive index n ℓ .As discussed elsewhere [16], h is fixed during deposition, while Ω and χ can bedetermined from scanning electron micrographs of the as-deposited chiral STF.Let ε a = ε a , ε b = ε b , and ε c = ε c for the as-deposited chiral STF. With theassumptions that (i) ε a ,b ,c have been measured through optical experiments,(ii) γ τ = 15, and (iii) the as-deposited chiral STF is a composite materialcomprising the deposited material and air, the inverse Bruggeman formalismcan be employed to determine n s , f s , and γ b [16]. Let us note that the effect ofincreasing γ τ beyond 10 is insignificant [15].3uppose next that ε a = ε a , ε b = ε b , and ε c = ε c for a chiral STF uniformlyinfiltrated by metal nanospheres and/or fluid nanospheres. The volume fractionof the metal is denoted by f np ∈ [0 , f ℓ = 1 − f np − f s ∈ [0 , n s , f s , γ b , and f np known, ε a ,b ,c can bedetermined using the forward Bruggeman formalism [19]. Obviously, f np = 0 ifthere are no metal nanoparticles [15, 16]. Furthermore, if the fluid is absent, wehave to set n ℓ = 1 while implementing the forward Bruggeman formalism. In order to formulate the canonical problem for SPP wave propagation [15], wetake the half space z < n met and the half space z > (a) (b) Figure 1: Schematics of (a) the canonical boundary-value problem, and (b) theTurbadar–Kretschmann–Raether prism-coupled configuration.The SPP wave is taken to propagate parallel to the unit vector ˆ u prop =ˆ u x cos ψ + ˆ u y sin ψ , ψ ∈ [0 , π ), in the xy plane and to decay far away fromthe interface z = 0. The electric and magnetic field phasors can be writteneverywhere as E ( x, y, z ) = e ( z ) exp[ iq ( x cos ψ + y sin ψ )] H ( x, y, z ) = h ( z ) exp[ iq ( x cos ψ + y sin ψ )] ) ,z ∈ ( −∞ , ∞ ) , (3)where the complex-valued wavenumber q and the vector functions e ( z ) and h ( z )are not known. The procedure to obtain a dispersion equation for q is providedin detail elsewhere [15, Chap. 3], and so is the procedure to determine thefunctions e ( z ) and h ( z ) for each solution q of the dispersion equation.4 .3 Prism-coupled configuration The prism-coupled configuration shown in Fig. 1(b) is practically implementable.Light of fixed polarization state and free-space wavelength λ is incident on thesemicircular face of the prism at an angle θ inc , the refractive index of the prismbeing denoted by n prism . The base of the prism is coated with a metal layerof thickness L met and refractive index n met . The other face of metal layer isin intimate contact with a chiral STF of thickness L d , beyond which is a halfspace occupied by the fluid. With I inc as the intensity of light inside the prismimpinging upon the prism/metal interface and I ref as the intensity of light in-side the prism reflected by the prism/metal interface, the detailed procedure todetermine the ratio R = I ref /I inc is available elsewhere [15].The minimums of R are identified as the angle θ inc ∈ [0 , π/
2) is varied. If acertain minimum occurs at the same value θ SPP of θ inc for all L d greater thansome threshold value while no transmission occurs in to the half space occupiedby the fluid, an SPP wave guided by the metal/chiral-STF interface is said tobe excited. Then, θ SPP = sin − (cid:20) Re ( q ) k n prism (cid:21) (4)ideally, where q is a solution of the dispersion equation of the canonical boundary-value problem. For all numerical results presented in this paper, we fixed λ = 633 nm andset ε a = 3 . ε b = 4 . ε c = 3 . χ = 58 . ◦ , in accordwith previous works [15, 16, 20]. The inverse Bruggeman formalism yields n s =3 . f s = 0 . γ b = 1 . h = 1, Ω = 200 nm, n prism = 2 . n met = 1 . . i (aluminum), L met = 15 nm,and n np = 0 . . i (silver). Without significant loss of generality, wefixed ψ = 0. The parameters L d , f np , and n ℓ ∈ [1 , .
5] were kept as variables.We confined the search for solutions to Re( q ) /k ∈ [1 , f np = 0 ) In order to assess the effects of metal nanoparticles residing inside a chiral STF,let us begin with the sensing of a fluid when f np = 0 [16].The real and imaginary parts of the relative wavenumbers q/k are plottedin Fig. 2 as functions of the refractive index n ℓ ∈ [1 , . v ph = ω/ Re( q ) and the propagation distance ∆ prop = 1 / Im( q ) in the xy plane.Values of θ SPP and the dynamic sensitivity [1] ρ = dθ SPP ( n ℓ ) dn ℓ (5)5or all three branches are plotted against n ℓ in Fig. 3, which shows that (i) θ inc isvery sensitive to changes in n ℓ and (ii) ρ can be as high as 30 deg/RIU (branch3). n l R e ( q ) / k (a) n l I m ( q ) / k (b) Figure 2: (a) Real and (b) imaginary parts of q/k plotted against n ℓ when f np = 0. The solutions found were organized in three branches labeled ‘1’, ‘2’,and ‘3’. SPP ( deg ) n l (a) ( deg / R I U ) n l (b) Figure 3: (a) θ SPP predicted for the prism-coupled configuration by using thedata of Fig. 2 in Eq. (4), and (b) the dynamic sensitivity ρ as a function of n ℓ for each branch when f np = 0. The acronym RIU stands for “refractive-indexunit”.When n ℓ = 1 .
33 (water), then SPP waves are predicted to be excited at θ SPP ∈ { . ◦ , . ◦ , . ◦ } in the prism-coupled configuration, according toFig. 3(a). Figure 4 presents the reflectances R p and R s as functions of θ inc for incident p - and s -polarized light, respectively, when L d ∈ { , , } .From Fig. 4(a), we conclude that SPP waves are excited at θ inc ∈ { . ◦ , . ◦ , . ◦ } because the angular locations of the minimums of R p are veryweakly dependent on L d when that thickness is large enough. We have alsoconfirmed that these angular locations do not change if L met is increased from15 nm to 20 nm. Similarly, from Fig. 4(b) we conclude that incident s -polarizedlight is able to excite an SPP wave at θ inc = 49 . ◦ . Thus, the predictions fromthe canonical boundary-value problem match the conclusions one can draw forthe prism-coupled configuration. 6 R p inc L d = 4 L d = 6 L d = 8 (a)
30 40 50 60 700.00.20.40.60.81.0 R s inc L d = 4 L d = 6 L d = 8 (b) Figure 4: Reflectances (a) R p and (b) R s as functions of θ inc for L d ∈{ , , } , when f np = 0 and n ℓ = 1 .
33. The arrows indicate the minimumsthat represent the excitation of SPP waves. f np > ) Let us now present results for f np >
0, i.e., when the chiral STF contains silvernanoparticles. In practice, f np must be very small or the chiral STF wouldbecome highly conducting, leading to the disappearance of SPP waves. Fortheoretical work, f np must be very small or the Bruggeman formalism will yieldunphysical results [19, 21]. n l R e ( q ) / k (a) n l I m ( q ) / k (b) Figure 5: Same as Fig. 2 except that the volume fraction of silver nanoparticlesis f np = 0 . q/k when f np = 0 . f np = 0 in Fig. 2, three branches of SPP waves exist in Fig. 5. Thepresence of the silver nanoparticles tends to reduce both the phase speed v ph and the propagation distance ∆ prop . Even more significantly, the higher- v ph branches 1 and 2 terminate at lower values of n ℓ when the silver nanoparticlesare present.Figure 6 provides the predicted values of θ SPP and ρ when f np = 0 .
01. Asindicated by Eq. (4) and confirmed by a comparison of Figs. 3 and 6, SPP wavesshould be excited by less obliquely incident light when the silver nanoparticlesare present. However, the maximum ρ increases from about 30 deg/RIU in7 .0 1.1 1.2 1.3 1.4 1.5304050607080 SPP ( deg ) n l (a) ( deg / R I U ) n l (b) Figure 6: Same as Fig. 3 except that the volume fraction of silver nanoparticlesis f np = 0 . f np = 0 to about 69 deg/RIU in Fig. 6(b) for f np = 0 .
01 forbranch 3.When n ℓ = 1 .
33, Fig. 6(a) indicates that SPP waves can be excited at θ SPP ∈ { . ◦ , . ◦ } in the prism-coupled configuration. Thus, the numberof SPP waves predicted reduces by unity when 1% volume of chiral STF isoccupied by the silver nanoparticles. This reduction is confirmed by the plots of R p versus θ inc in Fig. 7(a), the minimums of R p indicating SPP-wave excitationbeing located at θ inc ∈ { . ◦ , . ◦ } . Moreover, incident s -polarized light canexcite an SPP wave at θ inc = 54 . ◦ , according to Fig. 7(b).
30 40 50 60 700.00.20.40.60.81.0 R p inc L d = 4 L d = 6 L d = 8 (a)
30 40 50 60 700.00.20.40.60.81.0 R s inc L d = 4 L d = 6 L d = 8 (b) Figure 7: Same as Fig. 4 except that the volume fraction of silver nanoparticlesis f np = 0 . ρ , we have mapped it as a function of f np and n ℓ in Figs. 8-10 forthe three branches of the solutions. We chose n ℓ ∈ [1 . , . f np ≤ . n ℓ ∈ (1 . , .
6) and the change in ρ is very small. Forthe chosen prism and the chiral STF, the SPP waves on this branch are excitedwith θ SPP ∈ [ ∼ ◦ , ∼ ◦ ]. Figure 9 shows that on branch 2, (i) ρ can increasefrom about 22 deg/RIU to 46 deg/RIU and (ii) the detection over the entire8 .000 0.005 0.010 0.015 0.0201.301.351.401.451.501.551.60 n l f np (deg/RIU)22.0022.4022.8023.2023.6024.00 Figure 8: The dynamic sensitivity ρ as a function of the refractive index n ℓ of the fluid and the volume fraction f np of silver nanoparticles for solutions onbranch 1 in Figs. 2 and 5. n l f np (deg/RIU) Figure 9: Same as Fig. 8 except for branch 2. f np n l (deg/RIU)24.0046.2068.4090.60112.8135.0 Figure 10: Same as Fig. 8 except for branch 3.chosen range of n ℓ is possible only with f np ≤ .
008 with a maximum ρ ofabout 35 deg/RIU. Furthermore, the SPP waves on branch 2 are excited with9 SPP ∈ [ ∼ ◦ , ∼ ◦ ]. Finally, Fig. 10 that on branch 3, (i) ρ can increase up to135 deg/RIU, and (ii) the detection over the full chosen range of n ℓ is possibleonly with f np ≤ .
008 with a maximum ρ of about 98 deg/RIU. The SPP waveson branch 3 are excited with θ SPP ∈ [ ∼ ◦ , ∼ ◦ ]. To see if the enhancement of dynamic sensitivity is due to absorption lossinduced by silver nanoparticles in the chiral STF or if it is due to the neg-ative real part of the permittivity of the silver nanoparticles, we computed ρ when the silver nanoparticles of relative permittivity (0 . . i ) = − . . i are replaced by absorbing dielectric nanoparticles of relativepermittivity (4 . . i ) = 18 . . i . The data for f np = 0 . Also, we performed calculations with gold nanoparticles ( n np = 0 . . i )deployed instead of silver nanoparticles, while f np = 0 .
005 fixed and n ℓ ∈ [1 , . ρ being 24deg/RIU for branch 1 and 26 deg/RIU for branch 2. These values of maxi-mum ρ are much lower than those obtained with 0.5% volume fraction of silvernanoparticles: 54 deg/RIU for branch 1, 29 deg/RIU for branch 2, and 24deg/RIU for branch 3. ( deg / R I U ) n l Figure 11: Same as Fig. 6(b), except that silver nanoparticles of relative per-mittivity − . . i are replaced by absorbing dielectric nanoparticlesof relative permittivity 18 . . i .10 Concluding remarks
The multiple-SPP-waves-based sensing of a fluid uniformly infiltrating a chiralSTF impregnated with metal nanoparticles was studied theoretically, when thechiral STF is deployed in the prism-coupled configuration [1]. Comparison wasmade with the case when the nanoparticles are absent [16]. The Bruggemann ho-mogenization formalism was used in two different ways to model the three prin-cipal relative permittivity scalars of the metal-nanoparticle-impregnated chiralSTF flooded by the fluid.The main conclusion was that the dynamic sensitivity of the SPP-wave-basedoptical sensor can increase significantly when the chiral STF is impregnated withsilver nanoparticles, provided that the silver volume fraction does not exceedabout 1%. The enhancement in the dynamic sensitivity is not due to the ab-sorption introduced by the silver nanoparticles, and should be attributed tothe local-field enhancement due to the metal nanoparticles [10] and the pos-sible interaction of particle plasmon-polaritons and surface plasmon-polaritons[11, 12]. Gold nanoparticles did not enhance dynamic sensitivity as well as silvernanoparticles.