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Virtual Journal for Biomedical Optics

Virtual Journal for Biomedical Optics

| EXPLORING THE INTERFACE OF LIGHT AND BIOMEDICINE

  • Editors: Andrew Dunn and Anthony Durkin
  • Vol. 9, Iss. 4 — Apr. 1, 2014
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Giant circular dichroism enhancement and chiroptical illusion in hybrid molecule-plasmonic nanostructures

Yineng Liu, Rongyao Wang, and Xiangdong Zhang  »View Author Affiliations


Optics Express, Vol. 22, Issue 4, pp. 4357-4370 (2014)
http://dx.doi.org/10.1364/OE.22.004357


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Abstract

Recently, there are great interest in studying the interaction between chiral molecules and plasmonic particles, because a weak circular dichroism (CD) signal in the ultraviolet (UV) region from chiral molecules can be both enhanced and transferred to the visible wavelength range by using plasmonic particles. Thus, ultrasensitive probe of tiny amounts of chiral substance by CD are worth waiting for. Here we present another way to strongly enhance CD of chiral molecules by using plasmonic particle cluster, which need not transfer to the visible wavelength. The method to calculate CD of chiral molecules in nanosphere clusters has been developed by means of multiple scattering of electromagnetic multipole fields. Our calculated results show that 2 orders of magnitude CD enhancement in the UV region for chiral molecules can be realized. Such a CD enhancement is very sensitive to the cluster structure. The cluster structure can cause chiroptical illusion in which a mirror symmetry in the CD spectra of opposite enantiomeric molecules is broken. The correction of quantum size effect on the phenomenon has also been considered. Our findings open up an alternative avenue for the ultrasensitive detection and illusion of chiral information.

© 2014 Optical Society of America

1. Introduction

Chirality is an inherent phenomenon, which plays a pivotal role in biochemistry and the evolution of life itself [1

1. G. D. Fasman, Circular dichroism and the conformational analysis of biomolecules (Plenum, 1996).

, 2

2. G. H. Wagniere, On chirality and the universal asymmetry: reflections on image and mirror image (VHCA with Wiley-VCH, 2007).

]. Circular dichroism (CD) spectroscopy is one of the central methods to probe chiral nature of molecules through describing the difference in absorption of right- and left-handed circularly-polarized photons [3

3. N. Berova, P. L. Polavarapu, K. Nakanishi, and R. W. Woody, Comprehensive Chiroptical Spectroscopy (John Wiley and Sons Inc.: New York, 2012).

, 4

4. D. Patterson, M. Schnell, and J. M. Doyle, “Enantiomer-specific detection of chiral molecules via microwave spectroscopy,” Nature 497(7450), 475–477 (2013). [CrossRef] [PubMed]

]. In general, the CD signal of biomolecules is typically weak, thus, chiral analyses by such a spectroscopic technique have usually restricted to the analyst at a relatively high concentration [1

1. G. D. Fasman, Circular dichroism and the conformational analysis of biomolecules (Plenum, 1996).

4

4. D. Patterson, M. Schnell, and J. M. Doyle, “Enantiomer-specific detection of chiral molecules via microwave spectroscopy,” Nature 497(7450), 475–477 (2013). [CrossRef] [PubMed]

]. This is frequently an impediment for a practical use because an ultrasensitive probe of tiny amounts of chiral substance is highly demanding for practical biosensing applications in biomedical and pharmaceutical fields.

2. Theory and method

We consider here a hybrid system consisting of a molecule and a cluster with N metallic nanospheres as shown in Fig. 1
Fig. 1 Geometry of a hybrid single molecule-plasmonic nanostructure. The system is scattered by an incident polarized light. Here θi, ϕi and ri are the coordinates of the ith sphere in the spherical coordinate system, and the coordinates of the chiral molecule are marked by θd, ϕd and rd.
, which is excited by circularly polarized light E0(ω). The total absorption rate of the system can be expressed as [37

37. H. Zhang and A. O. Govorov, “Giant circular dichroism of a molecule in a region of strong plasmon resonances between two neighboring gold nanocrystals,” Phys. Rev. B 87(7), 075410 (2013). [CrossRef]

]
Q=Qmolecule+QNP,
(1)
where Qmolecule=ω0ρ22γ22 represents the absorption rate from the molecule, ω0 is the frequency of molecular transition, γij is the relaxation term and ρij is the matrix element of density matrix, which are obtained by solving the master equation for quantum states of molecules using the rotating wave approximation in the linear regime [37

37. H. Zhang and A. O. Govorov, “Giant circular dichroism of a molecule in a region of strong plasmon resonances between two neighboring gold nanocrystals,” Phys. Rev. B 87(7), 075410 (2013). [CrossRef]

]. QNP(ω)=2ωiIm(εNP)Ei,totin·Ei,totindV is the absorption rate from NPs, in which Ei,totin denotes the total field inside the ith nanosphere (i=1,2......N), εNP is the permittivity of NPs and the integral is taken over nanosphere volumes, εr,0 is the relative dielectric constant of background. A CD signal for the system is defined as the difference between absorption of left- and right-handed polarized light, which can be written as
CD=Q+QΩ,
(2)
where the averaging over the solid angle, Ω, is needed since hybrid nanosphere complexes have random orientations.Q+ and Q represent the rate of absorption for left- and right-handed polarized light, respectively. Q±=Qmolecule±+QNP±, where Qmolecule± and QNP± are the absorption rate for the molecule and the sphere cluster, respectively. In general, the total CD of the system can be divided into two parts,
CDtotal=CDmolecule+CDNP,
(3)
where CDmolecule=Qmolecule+QmoleculeΩ and CDNP=QNP+QNPΩ. Performing the averaging over Ω for CDmolecule [37

37. H. Zhang and A. O. Govorov, “Giant circular dichroism of a molecule in a region of strong plasmon resonances between two neighboring gold nanocrystals,” Phys. Rev. B 87(7), 075410 (2013). [CrossRef]

], we obtain
CDmolecule=8εr3cω0γ21|E0|2Im[m21.(P^+μ12)]|(ω-ω0)+iγ21-G|2
(4)
with
G=14πε0μ21i(Φiout.μ12)|r=rd,
(5)
where the function G originates from plasmonic surface charges of NPs induced by the molecule dipole, the vector Φiout=lmDlm,i1|r-ri|l+1Ylm(θr-ri,ϕr-ri) defines the electric potential induced by the surface charges of the ith sphere, Ylm is spherical harmonic, Dlm,i is expansion coefficient, which can be determined by the boundary conditions (see Appendix). The c represents light velocity in vacuum, μij and mij are matrix elements of the electric and magnetic dipolar moments [37

37. H. Zhang and A. O. Govorov, “Giant circular dichroism of a molecule in a region of strong plasmon resonances between two neighboring gold nanocrystals,” Phys. Rev. B 87(7), 075410 (2013). [CrossRef]

]. Here P^ is the field-enhancement matrices inside a molecule, which describes strong changes of the optical electric field inside a molecule due to the presence of NPs and is expressed as
P^=[pxxpxypxzpyxpyypyzpzxpzypzz].
(6)
The matrix elements (pβα) in Eq. (6) are determined from the relation: pβα=(Esc+E0)β/(E0)α, Esc is the scattering field at the position of the molecule from NPs in the cluster, which can be obtained by the multiple scattering method [38

38. J. Xu and X. D. Zhang, “Second harmonic generation in three-dimensional structures based on homogeneous centrosymmetric metallic spheres,” Opt. Express 20(2), 1668–1684 (2012). [CrossRef] [PubMed]

]. According to analysis in [37

37. H. Zhang and A. O. Govorov, “Giant circular dichroism of a molecule in a region of strong plasmon resonances between two neighboring gold nanocrystals,” Phys. Rev. B 87(7), 075410 (2013). [CrossRef]

], the CDNP mainly comes from two terms:CDNP=CDNP,dipole-field+CDNP,dipole-dipole. From the definition of QNP, we arrive at [37

37. H. Zhang and A. O. Govorov, “Giant circular dichroism of a molecule in a region of strong plasmon resonances between two neighboring gold nanocrystals,” Phys. Rev. B 87(7), 075410 (2013). [CrossRef]

]
CDNP,dipole-field=2ωεr3cπε0i(ImεNP)Imm21.[K^+(r)(iΦi,tot.μ21)](ω-ω0)+iγ21-GdV,
(7)
CDNP,dipole-diploe=8ωεr3c|E0|2Im[m21.(P^+μ12)]|(ωω0)+iγ21-G|2Im(G),
(8)
where
Φi,tot(r)=Φ0(i)+Φiin+jiΦjout,
(9)
Φjout=lml'm'Dl'm',jgl'm',lm(rj-ri)(r-ri)lYlm(θr-ri,ϕr-ri)
(10)
with
gl'm',lm(rj-ri)=l2m2l2-l1=l'4π(2l')!(-1)l2(2l2)!(2l1+1)!1|rj-ri|l2+1Clml2m2l'm'Yl2m2(θrj-ri,ϕrj-ri).
(11)
Here Φi,tot(r) is the total electric potential function inside the ith sphere, Φ0(i) is the potential induced by the isolated molecule, Φiin is the potential inside the ith sphere induced by the induced charge, Clml2m2l'm' is the expanded coefficient. Equations (9)-(11) are obtained by the addition theorem (see Appendix). The position-dependent matrix K^(r) determines the field inside NPs, which can be expressed as
K^=[krrkrθkrϕkθrkθθkθϕkϕrkϕθkϕϕ].
(12)
The matrix elements (kβα) in Eq. (12) are determined from the relation: kβα=(Esc)β/(E0)α. Based on the above equations, the CD of hybrid systems consisting of a molecule and nanosphere clusters can be obtained through numerical calculations.

3. Giant CD in the UV region

We first consider the case of two metallic spheres and a molecule. The CD for such a system has been discussed very well in [37

37. H. Zhang and A. O. Govorov, “Giant circular dichroism of a molecule in a region of strong plasmon resonances between two neighboring gold nanocrystals,” Phys. Rev. B 87(7), 075410 (2013). [CrossRef]

], which allows us to validate our calculated method. Figure 2(a)
Fig. 2 Calculated CD signals as a function of wavelengths for molecule-NP complexes with two spheres (a), two large spheres and one small sphere with d2=2nm (b), two large spheres and one small sphere with d2=1.5nm (c). Here d2 represent the distance between the molecule and small sphere, and d1=4nm is the distance between two large spheres. The radii of two large Au spheres are taken as 17.5nm, the radius for small Au sphere is taken as 4nm. In inset, θ=π/3 represents the angle between the orientation of molecular dipole and y axis. (d) Calculated extinctions of Au NPs.
shows our calculated CD signals as a function of wavelengths for a hybrid system consisting of a molecule and a gold dimer. Here the radii of two gold spheres are taken as 17.5nm and the separation between them is d1=4nm. The molecular linker located at the nanogap is idealized to be a single molecular dipole that is oriented at θ=π/3 as shown in inset of Fig. 2(a), θ is the angle between the orientation of molecular dipole and y axis. The parameters of the molecular dipole are taken according to [1

1. G. D. Fasman, Circular dichroism and the conformational analysis of biomolecules (Plenum, 1996).

37

37. H. Zhang and A. O. Govorov, “Giant circular dichroism of a molecule in a region of strong plasmon resonances between two neighboring gold nanocrystals,” Phys. Rev. B 87(7), 075410 (2013). [CrossRef]

]: μ12=|e|r12 and μ12m21/μ12=i|e|r0ω0r21/2. In our calculations, we use r12=2A0, r0=0.05A0 and γ12=0.3eV. For the dielectric functions of Au, the Palik’s data were adopted [39

39. E. D. Palik, Handbook of Optical Constants of Solids (Academic, 1985).

], the permittivity of water is taken as εr,0=1.8. The black line and red line correspond to CDmolecule and CDNP, respectively, the total CD is described by the green line. The resonance of molecules appears at λ=300nm, and the plasmon resonance for Au sphere is larger than 520nm, which can be seen clearly from extinction of the Au dimer (black line in Fig. 2(d)). Although a molecular exciton is off the plasmon resonance of a Au dimer, a small enhancement of the CD still appears. This is because the interference of incident and induced fields (Fano effect) [37

37. H. Zhang and A. O. Govorov, “Giant circular dichroism of a molecule in a region of strong plasmon resonances between two neighboring gold nanocrystals,” Phys. Rev. B 87(7), 075410 (2013). [CrossRef]

]. Our calculated results are identical with those in [37

37. H. Zhang and A. O. Govorov, “Giant circular dichroism of a molecule in a region of strong plasmon resonances between two neighboring gold nanocrystals,” Phys. Rev. B 87(7), 075410 (2013). [CrossRef]

].

However, the situation becomes different, if we put another Au sphere with radius 4nm near the dimer as shown in inset of Fig. 2(b). Figure 2(b) and 2(c) display calculated results of CD signals for the three-sphere system with d2=2nm and d2=1.5nm, respectively. Here d2 represents the distance between the molecule and the third sphere. It is seen clearly that the CDmolecule (black line) is improved largely although the CDNP (red line) is almost unchanged with the introduction of the third sphere, which results in the strong enhancement of total CD signals (green line) around λ=300nm. For example, the CD is improved 10 times at d2=2nm for the present case, it reaches 40 times at d2=1.5nm. Such an improvement of CD signal depends on the orientation of molecular dipole, which can be seen clearly from Fig. 3
Fig. 3 (a) Calculated CD signals as a function of wavelengths for molecule-NP complexes with two Au large spheres and one Au small sphere at various orientations of a molecular dipole. Here d2=2nm. (b) The corresponding CD signals for (a) as a function of orientations of a molecular dipole. The other parameters are identical with those in Fig. 2. The corresponding CD signals as a function of wavelengths and orientations of a molecular dipole for Ag sphere systems are given in (c) and (d), respectively. The sizes of Ag spheres and cluster structure are identical with those of three-sphere Au system.
.

Figure 3(a) shows calculated CD signals as a function of wavelengths for the three-sphere system at various orientations of the molecular dipole, the corresponding results as a function of orientation of the molecular dipole are described in Fig. 3(b). The smaller the value for θ, the greater increasing for CD. More than 2 orders of magnitude CD enhancement in the UV region are observed at small θ. Such a phenomenon does not own by Au particle clusters alone. Figure 3(c) and 3(d) show the corresponding results for silver sphere clusters. Here the radii of two large and one small Ag spheres are taken identical with those of three-sphere Au system, the separations among spheres are also the same. The Palik’s data are still adopted for the dielectric functions of Ag. Similar phenomenon is observed again.

At the same time, the nanostructure can also cause asymmetry of CD spectra. Figure 6(a)
Fig. 6 Calculated CD signals as a function of wavelengths for molecule-NP complexes with two large spheres and one small sphere at d2=2nm. (a) left-opened structure with molecular orientation at θ=π/3, (b) right-opened structure with molecular orientation at θ=π/3, (c) right-opened structure with molecular orientation at θ=4π/3. The other parameters are identical with those in Fig. 2.
describes the case of three-sphere system at θ=π/3 when the small sphere locates at the right side of the dimer (left-opened structure), whereas the corresponding results are given in Fig. 6(b) when the small sphere locates at the left side of the dimer (right-opened structure). Comparing them, we find that the CD spectra exhibit different features although extinctions for two kinds of structure without chiral molecules are the same. This also leads to another kind of interesting phenomenon, that is, the nanostructure causes mirror symmetry breaking of CD spectra.

In general, an enantiomeric pair of chiral molecule possesses CD spectra with a mirror symmetry, as shown in inset of Fig. 6(c). Here the enantiomeric pair are denoted by the molecular dipoles with opposite sign of μ12. Figure 6(c) shows calculated CD signals for the right-opened structure at θ=4π/3. Comparing Fig. 6(c) with Fig. 6(a), we find that the mirror symmetry of CD spectra does not exist. Originally a chiral molecule such as left-handed molecule should possess a negative CD signal around λ=300nm, when the nanostructure introduces, it exhibits a positive CD signal. Such a reversion of CD band means that nanostructures can cause chiroptical illusion of molecular CD signature. Also noteworthy that native CD response of a chiral molecule is normally of a broad band-width spanning the range of molecular resonant absorptions. In contrast, the present enhanced CD signal shows a very sharp peak around the wavelength of molecule resonances. This advantage may offer a very big superiority for a high spectral resolution of chiral probe of biomolecules, since biomolecules like proteins usually have very complicated structures of CD spectrum.

4. Effect of quantum size on CD

Recent investigations show that as the nanoparticle radii below 10 nm or the gap between two metal spheres is smaller than 0.8nm, the effect of quantum size on the plasmon resonance becomes important [40

40. J. Zuloaga, E. Prodan, and P. Nordlander, “Quantum Description of the plasmon resonances of a nanoparticle Dimer,” Nano Lett. 9(2), 887–891 (2009). [PubMed]

44

44. R. A. de la Osa, J. M. Sanz, J. M. Saiz, F. González, and F. Moreno, “Quantum optical response of metallic nanoparticles and dimers,” Opt. Lett. 37(23), 5015–5017 (2012). [CrossRef] [PubMed]

]. For above some cases, we consider 4nm radius sphere, quantum corrections are required due to the size of the particles. In the following, we consider the effect of quantum size on the CD signals. Considering quantum size effects of small particles, we model the conduction electrons as a free electron gas constrained by infinite potential barriers at the physical edges of the particle according to [42

42. J. A. Scholl, A. L. Koh, and J. A. Dionne, “Quantum plasmon resonances of individual metallic nanoparticles,” Nature 483(7390), 421–427 (2012). [CrossRef] [PubMed]

44

44. R. A. de la Osa, J. M. Sanz, J. M. Saiz, F. González, and F. Moreno, “Quantum optical response of metallic nanoparticles and dimers,” Opt. Lett. 37(23), 5015–5017 (2012). [CrossRef] [PubMed]

]. The standard Drude model is recast with Lorentzian terms that can be defined quantum mechanically, the particle permittivity can be expressed as [45

45. W. A. Kraus and G. C. Schatz, “Plasmon resonance broadending in small metal particles,” J. Chem. Phys. 79(12), 6130–6139 (1983). [CrossRef]

]:
ε(ω)=εIB+ωp2ifSifωif2ω2iγω,
(13)
where εIB is a frequency-dependent correction term to account for the contribution of the d-band valence electrons to interband transitions at higher energies, ωp is the plasma frequency, and γ is the scattering frequency, dependent on the nanosphere dimension (particle radius) and the empirical constant. ωif and Sif represent electron transition frequencies and oscillator strengths, respectively.

Based on Eq. (13), we recalculate CD signals for the three-sphere system with d2=1.5nm as given in Fig. 2. The calculated results are plotted in Fig. 7
Fig. 7 Comparison between classical and QM-corrected results for calculated CD signals as a function of wavelengths for molecule-NP complexes with two large spheres and one small sphere at d2=1.5nm. The black line corresponds to classical results, red line is QM-corrected results, green line is the results with QM correction at d2=1.4nm.
. The red dashed line in Fig. 7 represents the result with the quantum size correction, comparing it with classical result (black line) we find that blue shift of enhanced peak occurs, the amplitude of the peak also decreases. However, we change slightly the position of the third sphere, for example, as d2=1.4nm, the same amplitude enhancement of CD (green dotted line) is observed again. This means that the phenomena disclosed in the above calculations always appear even considering the quantum effect.

5. Summary

We have presented a multiple scattering method to calculate CD signals of the hybrid system consisting of a molecule and nanosphere cluster. The CD spectra for a chiral molecule inserted into clusters with various metallic nanospheres have been calculated. Our calculated results show that giant enhanced CD of the molecule in the UV region, more than 2 orders of magnitude enhancement in some cases, can be realized by using metallic nanosphere clusters. The enhanced CD resonances are very sensitive to structures and symmetries of the cluster, and they are also very sharp around the wavelength of molecule resonances. Thus, it brings some advantages to perform direct ultrasensitive detection on the chiral molecule in the UV region, which need not transfer to the visible wavelength. Furthermore, we have also found that the mirror symmetry of CD signals can be broken by introducing nanostructures. Therefore, the chiroptical illusion phenomenon of CD signals caused by nanostructures has been disclosed. In addition, quantum size correction on the phenomenon has also been considered. The physical origin for the phenomena has been analyzed. The proposed effects offer an alternative avenue for the ultrasensitive probing of chiral molecules in the UV region.

Appendix

In this appendix we present formalism and solution for Dlm,i,Φi,tot(r) and G. First let us consider electric potential induced only by molecular dipole. Supposing the molecule is placed in the position rd=(rd,θd,ϕd), the molecular dipole moment is d, then the electric potential is expressed as
φ0=14πε0drr3.
(14)
If we define the center of ith NP as r1=(ri,θi,ϕi), the electric potential is written as
Φ0(i)=lmBlm,i(4π2l+1)|r-ri|lrd,il+2Ylm(θr-ri,ϕr-ri)(rd,i=|rd-ri|).
(15)
By the formula
rr3=-(1r)
(16)
and
1|r-r'|=l=0m=-ll(4π2l+1)r<lr>l+1Ylm*(θ',ϕ')Ylm(θ,ϕ),
(17)
we can obtain the coefficients:
Bθlm,i=θ'[Ylm*(θ',ϕ')]θ'=θrd-ri,ϕ=ϕrd-riBϕlm,i=1sinθ'ϕ'[Ylm*(θ',ϕ')]θ'=θrd-ri,ϕ=ϕrd-riBrlm,i=-(l+1)[Ylm*(θ',ϕ')]θ'=θrd-ri,ϕ=ϕrd-ri
(18)
and

[Blm,ixBlm,iyBlm,iz]=[sinθcosϕcosθcosϕ-sinϕsinθsinϕcosθsinϕcosϕcosθ-sinθ0]θ'=θrd-ri,ϕ=ϕrd-ri[Blm,irBlm,iθBlm,iϕ].
(19)

Now we investigate the electric potential induced by dipole moment in the presence of NP cluster. The electric potential functions for ith and jth spheres induced by dipole moment, Φi and Φj, can be expressed as
Φi={lmDlm,i1|r-ri|l+1Ylm(θr-ri,ϕr-ri)(|r-ri|Ri),ΦioutlmDlm,i|r-ri|lRi2l+1Ylm(θr-ri,ϕr-ri)(|r-ri|Ri),ΦiinΦj={lmDlm,j1|r-rj|l+1Ylm(θr-rj,ϕr-rj)(|r-rj|Rj),ΦjoutlmDlm,j|r-rj|lRj2l+1Ylm(θr-rj,ϕr-rj)(|r-rj|Rj),Φjin.
(20)
By using the following addition formalism for potentials:
{Yl1(θ1,ϕ1)Yl2(θ2,ϕ2)}lm=m1,m2Cl1m1l2m2lmYl1m1(θ1,ϕ1)Yl2m2(θ2,ϕ2),
(21)
1rl+1Ylm(θ,ϕ)=4π(2l)!l1,l2=0l2-l1=ll(-1)l2(2l2)!(2l1+1)!r1l1r2l2+1{Yl1(θ1,ϕ1)Yl2(θ2,ϕ2)}lm,
(22)
performing the following coordinate transformation:
1|r-rj|l+1Ylm(θr-rj,ϕr-rj)=1|(r-ri)-(rj-ri)|l+1Ylm(θ(r-ri)-(rj-ri),ϕ(r-ri)-(rj-ri))=4π(2l)!l1,l2=0l2-l1=ll(-1)l2(2l2)!(2l1+1)!|r-ri|l1|rj-ri|l2+1m1,m2Cl1m1l2m2lmYl1m1(θr-ri,ϕr-ri)Yl2m2(θrj-ri,ϕrj-ri),=l1m1glm,l1m1(rj-ri)(r-ri)l1Yl1m1(θr-ri,ϕr-ri)
(23)
with
glm,l1m1(rj-ri)=l2m2l2-l1=l4π(2l)!(-1)l2(2l2)!(2l1+1)!1|rj-ri|l2+1Cl1m1l2m2lmYl2m2(θrj-ri,ϕrj-ri),
(24)
we obtain:
l'm'Dl'm',j1|r-rj|l'+1Yl'm'(θr-rj,ϕr-rj)=l'm'Dl'm',j1|(r-ri)-(rj-ri)|l'+1Yl'm'(θ(r-ri)-(rj-ri),ϕ(r-ri)-(rj-ri))=lml'm'Dl'm',jgl'm',lm(rj-ri)(r-ri)lYlm(θr-ri,ϕr-ri)
(25)
with
gl'm',lm(rj-ri)=l2m2l2-l1=l'4π(2l')!(-1)l2(2l2)!(2l1+1)!1|rj-ri|l2+1Clml2m2l'm'Yl2m2(θrj-ri,ϕrj-ri).
(26)
Then
φjout=lmDlm,j1|r-rj|l+1Ylm(θr-rj,ϕr-rj)=lml'm'Dl'm',jgl'm',lm(rj-ri)(r-ri)lYlm(θr-ri,ϕr-ri),
(27)
where
gl'm',lm(rj-ri)=l2m2l2-l1=l'4π(2l')!(-1)l2(2l2)!(2l1+1)!1|rj-ri|l2+1Clml2m2l'm'Yl2m2(θrj-ri,ϕrj-ri).
(28)
By using boundary conditions:εNPφir|r=R0+=ε0φir|r=R+0+, we obtain
εNP{Blm,i(4π2l+1)l|r-ri|l-1rd,il+2+Dlm,il|r-ri|l-1Ri2l+1}Ylm(θr-ri,ϕr-ri)+εNP[l'm'jiDl'm',jgl'm',lm(rj-ri)]l(r-ri)l-1Ylm(θr-ri,ϕr-ri)=ε0{Blm,i(4π2l+1)l|r-ri|l-1rd,il+2+Dlm,i-(l+1)|r-ri|l+2}Ylm(θr-ri,ϕr-ri)+ε0[l'm'jiDl'm',jgl'm',lm(rj-ri)]l(r-ri)l-1Ylm(θr-ri,ϕr-ri)|r-ri=RiεNPBlm,i(4π2l+1)lRil-1rd,il+2+Dlm,iεNPlRil+2+εNP[l'm'jiDl'm',jgl'm',lm(rj-ri)]lRil-1=ε0Blm,i(4π2l+1)lRil-1rd,il+2+Dlm,i-(l+1)ε0Ril+2+ε0[l'm'jiDl'm',jgl'm',lm(rj-ri)]lRil-1.
(29)
To solve Eq. (29), we obtain Dlm,i, then Φi,tot(r) and G can be obtained.

Acknowledgments

We wish to thank Hui Zhang for useful discussions. This work was supported by the National Natural Science Foundation of China (Grant No. 11274042) and the National Key Basic Research Special Foundation of China under Grant 2013CB632704.

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F. J. García de Abajo, “Rev. Colloquium: Light scattering by particle and hole arrays,” Rev. Mod. Phys. 79(4), 1267–1290 (2007). [CrossRef]

11.

S. K. Ghosh and T. Pal, “Interparticle coupling effect on the surface plasmon resonance of gold nanoparticles: from theory to applications,” Chem. Rev. 107(11), 4797–4862 (2007). [CrossRef] [PubMed]

12.

K. A. Willets, V. Duyne, and R. P. Annu, “Localized surface plasmon resonance spectroscopy and sensing,” J. Phys. Chem. 58(1), 267–297 (2007).

13.

E. Hendry, T. Carpy, J. Johnston, M. Popland, R. V. Mikhaylovskiy, A. J. Lapthorn, S. M. Kelly, L. D. Barron, N. Gadegaard, and M. Kadodwala, “Ultrasensitive detection and characterization of biomolecules using superchiral fields,” Nat. Nanotechnol. 5(11), 783–787 (2010). [CrossRef] [PubMed]

14.

S. Nie and S. R. Emory, “Probing Single Molecules and Single Nanoparticles by Surface-Enhanced Raman Scattering,” Science 275(5303), 1102–1106 (1997). [CrossRef] [PubMed]

15.

H. Xu, E. J. Bjerneld, M. Kall, and L. Borjesson, “Spectroscopy of Single Hemoglobin Molecules by Surface Enhanced Raman Scattering,” Phys. Rev. Lett. 83(21), 4357–4360 (1999). [CrossRef]

16.

L. Chuntonov and G. Haran, “Maximal Raman Optical Activity in Hybrid Single Molecule-Plasmonic Nanostructures with Multiple Dipolar Resonances,” Nano Lett. 13(3), 1285–1290 (2013). [CrossRef] [PubMed]

17.

V. E. Ferry, L. A. Sweatlock, D. Pacifici, and H. A. Atwater, “Plasmonic Nanostructure Design for Efficient Light Coupling into Solar Cells,” Nano Lett. 8(12), 4391–4397 (2008). [CrossRef] [PubMed]

18.

C. Rockstuhl and F. Lederer, “Photon management by metallic nanodiscs in thin film solar cells,” Appl. Phys. Lett. 94(21), 213102 (2009). [CrossRef]

19.

M. Kuwata-Gonokami, N. Saito, Y. Ino, M. Kauranen, K. Jefimovs, T. Vallius, J. Turunen, and Y. Svirko, “Giant Optical Activity in Quasi-Two-Dimensional Planar Nanostructures,” Phys. Rev. Lett. 95(22), 227401 (2005). [CrossRef] [PubMed]

20.

I. Lieberman, G. Shemer, T. Fried, E. M. Kosower, and G. Markovich, “Plasmon-resonance-enhanced absorption and circular dichroism,” Angew. Chem. Int. Ed. Engl. 47(26), 4855–4857 (2008). [CrossRef] [PubMed]

21.

J. George and K. G. Thomas, “Surface plasmon coupled circular dichroism of Au nanoparticles on peptide nanotubes,” J. Am. Chem. Soc. 132(8), 2502–2503 (2010). [CrossRef] [PubMed]

22.

Z. Li, Z. Zhu, W. Liu, Y. Zhou, B. Han, Y. Gao, and Z. Tang, “Reversible plasmonic circular dichroism of Au nanorod and DNA assemblies,” J. Am. Chem. Soc. 134(7), 3322–3325 (2012). [CrossRef] [PubMed]

23.

S. Zhang, H. Wei, K. Bao, U. Håkanson, N. J. Halas, P. Nordlander, and H. Xu, “Chiral Surface Plasmon Polaritons on Metallic Nanowires,” Phys. Rev. Lett. 107(9), 096801 (2011). [CrossRef] [PubMed]

24.

A. O. Govorov, Z. Fan, P. Hernandez, J. M. Slocik, and R. R. Naik, “Theory of Circular Dichroism of Nanomaterials Comprising Chiral Molecules and Nanocrystals: Plasmon Enhancement, Dipole Interactions, and Dielectric Effects,” Nano Lett. 10(4), 1374–1382 (2010). [CrossRef] [PubMed]

25.

Z. Fan and A. O. Govorov, “Plasmonic Circular Dichroism of Chiral Metal Nanoparticle Assemblies,” Nano Lett. 10(7), 2580–2587 (2010). [CrossRef] [PubMed]

26.

J. M. Slocik, A. O. Govorov, and R. R. Naik, “Plasmonic Circular Dichroism of Peptide-Functionalized Gold Nanoparticles,” Nano Lett. 11(2), 701–705 (2011). [CrossRef] [PubMed]

27.

B. M. Maoz, R. van der Weegen, Z. Fan, A. O. Govorov, G. Ellestad, N. Berova, E. W. Meijer, and G. Markovich, “Plasmonic chiroptical response of silver nanoparticles interacting with chiral supramolecular assemblies,” J. Am. Chem. Soc. 134(42), 17807–17813 (2012). [CrossRef] [PubMed]

28.

R.-Y. Wang, H. Wang, X. Wu, Y. Ji, P. Wang, Y. Qu, and T.-S. Chung, “Chiral assembly of gold nanorods with collective plasmomic circular dichroism response,” Soft Matter 7(18), 8370–8375 (2011). [CrossRef]

29.

N. Cathcart and V. Kitaev, “Monodisperse hexagonal silver nanoprisms: synthesis via thiolate-protected cluster precursors and chiral, ligand-imprinted self-assembly,” ACS Nano 5(9), 7411–7425 (2011). [CrossRef] [PubMed]

30.

V. V. Klimov, D. V. Guzatov, and M. Ducloy, “Engineering of radiation of optically active molecules with chiral nano-meta-particles,” Europhys. Lett. 97(4), 47004–47009 (2012). [CrossRef]

31.

M. Hentschel, M. Schäferling, T. Weiss, N. Liu, and H. Giessen, “Three-Dimensional Chiral Plasmonic Oligomers,” Nano Lett. 12(5), 2542–2547 (2012). [CrossRef] [PubMed]

32.

A. Kuzyk, R. Schreiber, Z. Fan, G. Pardatscher, E.-M. Roller, A. Högele, F. C. Simmel, A. O. Govorov, and T. Liedl, “DNA-based self-assembly of chiral plasmonic nanostructures with tailored optical response,” Nature 483(7389), 311–314 (2012). [CrossRef] [PubMed]

33.

Z. Xu, L. Xu, Y. Zhu, W. Ma, H. Kuang, L. Wang, and C. Xu, “Chirality based sensor for bisphenol A Detection,” Chem. Commun. (Camb.) 48(46), 5760–5762 (2012). [CrossRef] [PubMed]

34.

W. Yan, L. Xu, C. Xu, W. Ma, H. Kuang, L. Wang, and N. A. Kotov, “Self-Assembly of Chiral Nanoparticle Pyramids with Strong R/S Optical Activity,” J. Am. Chem. Soc. 134(36), 15114–15121 (2012). [CrossRef] [PubMed]

35.

B. M. Maoz, Y. Chaikin, A. B. Tesler, O. Bar Elli, Z. Fan, A. O. Govorov, and G. Markovich, “Amplification of Chiroptical Activity of Chiral Biomolecules by Surface Plasmons,” Nano Lett. 13(3), 1203–1209 (2013). [CrossRef] [PubMed]

36.

F. Lu, Y. Tian, M. Liu, D. Su, H. Zhang, A. O. Govorov, and O. Gang, “Discrete Nanocubes as Plasmonic Reporters of Molecular Chirality,” Nano Lett. 13(7), 3145–3151 (2013). [CrossRef] [PubMed]

37.

H. Zhang and A. O. Govorov, “Giant circular dichroism of a molecule in a region of strong plasmon resonances between two neighboring gold nanocrystals,” Phys. Rev. B 87(7), 075410 (2013). [CrossRef]

38.

J. Xu and X. D. Zhang, “Second harmonic generation in three-dimensional structures based on homogeneous centrosymmetric metallic spheres,” Opt. Express 20(2), 1668–1684 (2012). [CrossRef] [PubMed]

39.

E. D. Palik, Handbook of Optical Constants of Solids (Academic, 1985).

40.

J. Zuloaga, E. Prodan, and P. Nordlander, “Quantum Description of the plasmon resonances of a nanoparticle Dimer,” Nano Lett. 9(2), 887–891 (2009). [PubMed]

41.

R. Esteban, A. G. Borisov, P. Nordlander, and J. Aizpurua, “Bridging quantum and classical plasmonics with a quantum-corrected model,” Nat Commun 3, 825 (2012). [CrossRef] [PubMed]

42.

J. A. Scholl, A. L. Koh, and J. A. Dionne, “Quantum plasmon resonances of individual metallic nanoparticles,” Nature 483(7390), 421–427 (2012). [CrossRef] [PubMed]

43.

K. J. Savage, M. M. Hawkeye, R. Esteban, A. G. Borisov, J. Aizpurua, and J. J. Baumberg, “Revealing the quantum regime in tunnelling plasmonics,” Nature 491(7425), 574–577 (2012). [CrossRef] [PubMed]

44.

R. A. de la Osa, J. M. Sanz, J. M. Saiz, F. González, and F. Moreno, “Quantum optical response of metallic nanoparticles and dimers,” Opt. Lett. 37(23), 5015–5017 (2012). [CrossRef] [PubMed]

45.

W. A. Kraus and G. C. Schatz, “Plasmon resonance broadending in small metal particles,” J. Chem. Phys. 79(12), 6130–6139 (1983). [CrossRef]

OCIS Codes
(240.6680) Optics at surfaces : Surface plasmons
(280.1415) Remote sensing and sensors : Biological sensing and sensors

ToC Category:
Plasmonics

History
Original Manuscript: January 3, 2014
Manuscript Accepted: February 10, 2014
Published: February 18, 2014

Virtual Issues
Vol. 9, Iss. 4 Virtual Journal for Biomedical Optics

Citation
Yineng Liu, Rongyao Wang, and Xiangdong Zhang, "Giant circular dichroism enhancement and chiroptical illusion in hybrid molecule-plasmonic nanostructures," Opt. Express 22, 4357-4370 (2014)
http://www.opticsinfobase.org/vjbo/abstract.cfm?URI=oe-22-4-4357


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References

  1. G. D. Fasman, Circular dichroism and the conformational analysis of biomolecules (Plenum, 1996).
  2. G. H. Wagniere, On chirality and the universal asymmetry: reflections on image and mirror image (VHCA with Wiley-VCH, 2007).
  3. N. Berova, P. L. Polavarapu, K. Nakanishi, and R. W. Woody, Comprehensive Chiroptical Spectroscopy (John Wiley and Sons Inc.: New York, 2012).
  4. D. Patterson, M. Schnell, J. M. Doyle, “Enantiomer-specific detection of chiral molecules via microwave spectroscopy,” Nature 497(7450), 475–477 (2013). [CrossRef] [PubMed]
  5. M. Bruchez, M. Moronne, P. Gin, S. Weiss, A. P. Alivisatos, “Semiconductor Nanocrystals as Fluorescent Biological Labels,” Science 281(5385), 2013–2016 (1998). [CrossRef] [PubMed]
  6. W. C. W. Chan, S. Nie, “Quantum Dot Bioconjugates for Ultrasensitive Nonisotopic Detection,” Science 281(5385), 2016–2018 (1998). [CrossRef] [PubMed]
  7. E. Prodan, C. Radloff, N. J. Halas, P. Nordlander, “A Hybridization Model for the Plasmon Response of Complex Nanostructures,” Science 302(5644), 419–422 (2003). [CrossRef] [PubMed]
  8. W. J. Crookes-Goodson, J. M. Slocik, R. R. Naik, “Bio-directed synthesis and assembly of nanomaterials,” Chem. Soc. Rev. 37(11), 2403–2412 (2008). [CrossRef] [PubMed]
  9. Y. Tang, M. Ouyang, “Tailoring properties and functionalities of metal nanoparticles through crystallinity engineering,” Nat. Mater. 6(10), 754–759 (2007). [CrossRef] [PubMed]
  10. F. J. García de Abajo, “Rev. Colloquium: Light scattering by particle and hole arrays,” Rev. Mod. Phys. 79(4), 1267–1290 (2007). [CrossRef]
  11. S. K. Ghosh, T. Pal, “Interparticle coupling effect on the surface plasmon resonance of gold nanoparticles: from theory to applications,” Chem. Rev. 107(11), 4797–4862 (2007). [CrossRef] [PubMed]
  12. K. A. Willets, V. Duyne, R. P. Annu, “Localized surface plasmon resonance spectroscopy and sensing,” J. Phys. Chem. 58(1), 267–297 (2007).
  13. E. Hendry, T. Carpy, J. Johnston, M. Popland, R. V. Mikhaylovskiy, A. J. Lapthorn, S. M. Kelly, L. D. Barron, N. Gadegaard, M. Kadodwala, “Ultrasensitive detection and characterization of biomolecules using superchiral fields,” Nat. Nanotechnol. 5(11), 783–787 (2010). [CrossRef] [PubMed]
  14. S. Nie, S. R. Emory, “Probing Single Molecules and Single Nanoparticles by Surface-Enhanced Raman Scattering,” Science 275(5303), 1102–1106 (1997). [CrossRef] [PubMed]
  15. H. Xu, E. J. Bjerneld, M. Kall, L. Borjesson, “Spectroscopy of Single Hemoglobin Molecules by Surface Enhanced Raman Scattering,” Phys. Rev. Lett. 83(21), 4357–4360 (1999). [CrossRef]
  16. L. Chuntonov, G. Haran, “Maximal Raman Optical Activity in Hybrid Single Molecule-Plasmonic Nanostructures with Multiple Dipolar Resonances,” Nano Lett. 13(3), 1285–1290 (2013). [CrossRef] [PubMed]
  17. V. E. Ferry, L. A. Sweatlock, D. Pacifici, H. A. Atwater, “Plasmonic Nanostructure Design for Efficient Light Coupling into Solar Cells,” Nano Lett. 8(12), 4391–4397 (2008). [CrossRef] [PubMed]
  18. C. Rockstuhl, F. Lederer, “Photon management by metallic nanodiscs in thin film solar cells,” Appl. Phys. Lett. 94(21), 213102 (2009). [CrossRef]
  19. M. Kuwata-Gonokami, N. Saito, Y. Ino, M. Kauranen, K. Jefimovs, T. Vallius, J. Turunen, Y. Svirko, “Giant Optical Activity in Quasi-Two-Dimensional Planar Nanostructures,” Phys. Rev. Lett. 95(22), 227401 (2005). [CrossRef] [PubMed]
  20. I. Lieberman, G. Shemer, T. Fried, E. M. Kosower, G. Markovich, “Plasmon-resonance-enhanced absorption and circular dichroism,” Angew. Chem. Int. Ed. Engl. 47(26), 4855–4857 (2008). [CrossRef] [PubMed]
  21. J. George, K. G. Thomas, “Surface plasmon coupled circular dichroism of Au nanoparticles on peptide nanotubes,” J. Am. Chem. Soc. 132(8), 2502–2503 (2010). [CrossRef] [PubMed]
  22. Z. Li, Z. Zhu, W. Liu, Y. Zhou, B. Han, Y. Gao, Z. Tang, “Reversible plasmonic circular dichroism of Au nanorod and DNA assemblies,” J. Am. Chem. Soc. 134(7), 3322–3325 (2012). [CrossRef] [PubMed]
  23. S. Zhang, H. Wei, K. Bao, U. Håkanson, N. J. Halas, P. Nordlander, H. Xu, “Chiral Surface Plasmon Polaritons on Metallic Nanowires,” Phys. Rev. Lett. 107(9), 096801 (2011). [CrossRef] [PubMed]
  24. A. O. Govorov, Z. Fan, P. Hernandez, J. M. Slocik, R. R. Naik, “Theory of Circular Dichroism of Nanomaterials Comprising Chiral Molecules and Nanocrystals: Plasmon Enhancement, Dipole Interactions, and Dielectric Effects,” Nano Lett. 10(4), 1374–1382 (2010). [CrossRef] [PubMed]
  25. Z. Fan, A. O. Govorov, “Plasmonic Circular Dichroism of Chiral Metal Nanoparticle Assemblies,” Nano Lett. 10(7), 2580–2587 (2010). [CrossRef] [PubMed]
  26. J. M. Slocik, A. O. Govorov, R. R. Naik, “Plasmonic Circular Dichroism of Peptide-Functionalized Gold Nanoparticles,” Nano Lett. 11(2), 701–705 (2011). [CrossRef] [PubMed]
  27. B. M. Maoz, R. van der Weegen, Z. Fan, A. O. Govorov, G. Ellestad, N. Berova, E. W. Meijer, G. Markovich, “Plasmonic chiroptical response of silver nanoparticles interacting with chiral supramolecular assemblies,” J. Am. Chem. Soc. 134(42), 17807–17813 (2012). [CrossRef] [PubMed]
  28. R.-Y. Wang, H. Wang, X. Wu, Y. Ji, P. Wang, Y. Qu, T.-S. Chung, “Chiral assembly of gold nanorods with collective plasmomic circular dichroism response,” Soft Matter 7(18), 8370–8375 (2011). [CrossRef]
  29. N. Cathcart, V. Kitaev, “Monodisperse hexagonal silver nanoprisms: synthesis via thiolate-protected cluster precursors and chiral, ligand-imprinted self-assembly,” ACS Nano 5(9), 7411–7425 (2011). [CrossRef] [PubMed]
  30. V. V. Klimov, D. V. Guzatov, M. Ducloy, “Engineering of radiation of optically active molecules with chiral nano-meta-particles,” Europhys. Lett. 97(4), 47004–47009 (2012). [CrossRef]
  31. M. Hentschel, M. Schäferling, T. Weiss, N. Liu, H. Giessen, “Three-Dimensional Chiral Plasmonic Oligomers,” Nano Lett. 12(5), 2542–2547 (2012). [CrossRef] [PubMed]
  32. A. Kuzyk, R. Schreiber, Z. Fan, G. Pardatscher, E.-M. Roller, A. Högele, F. C. Simmel, A. O. Govorov, T. Liedl, “DNA-based self-assembly of chiral plasmonic nanostructures with tailored optical response,” Nature 483(7389), 311–314 (2012). [CrossRef] [PubMed]
  33. Z. Xu, L. Xu, Y. Zhu, W. Ma, H. Kuang, L. Wang, C. Xu, “Chirality based sensor for bisphenol A Detection,” Chem. Commun. (Camb.) 48(46), 5760–5762 (2012). [CrossRef] [PubMed]
  34. W. Yan, L. Xu, C. Xu, W. Ma, H. Kuang, L. Wang, N. A. Kotov, “Self-Assembly of Chiral Nanoparticle Pyramids with Strong R/S Optical Activity,” J. Am. Chem. Soc. 134(36), 15114–15121 (2012). [CrossRef] [PubMed]
  35. B. M. Maoz, Y. Chaikin, A. B. Tesler, O. Bar Elli, Z. Fan, A. O. Govorov, G. Markovich, “Amplification of Chiroptical Activity of Chiral Biomolecules by Surface Plasmons,” Nano Lett. 13(3), 1203–1209 (2013). [CrossRef] [PubMed]
  36. F. Lu, Y. Tian, M. Liu, D. Su, H. Zhang, A. O. Govorov, O. Gang, “Discrete Nanocubes as Plasmonic Reporters of Molecular Chirality,” Nano Lett. 13(7), 3145–3151 (2013). [CrossRef] [PubMed]
  37. H. Zhang, A. O. Govorov, “Giant circular dichroism of a molecule in a region of strong plasmon resonances between two neighboring gold nanocrystals,” Phys. Rev. B 87(7), 075410 (2013). [CrossRef]
  38. J. Xu, X. D. Zhang, “Second harmonic generation in three-dimensional structures based on homogeneous centrosymmetric metallic spheres,” Opt. Express 20(2), 1668–1684 (2012). [CrossRef] [PubMed]
  39. E. D. Palik, Handbook of Optical Constants of Solids (Academic, 1985).
  40. J. Zuloaga, E. Prodan, P. Nordlander, “Quantum Description of the plasmon resonances of a nanoparticle Dimer,” Nano Lett. 9(2), 887–891 (2009). [PubMed]
  41. R. Esteban, A. G. Borisov, P. Nordlander, J. Aizpurua, “Bridging quantum and classical plasmonics with a quantum-corrected model,” Nat Commun 3, 825 (2012). [CrossRef] [PubMed]
  42. J. A. Scholl, A. L. Koh, J. A. Dionne, “Quantum plasmon resonances of individual metallic nanoparticles,” Nature 483(7390), 421–427 (2012). [CrossRef] [PubMed]
  43. K. J. Savage, M. M. Hawkeye, R. Esteban, A. G. Borisov, J. Aizpurua, J. J. Baumberg, “Revealing the quantum regime in tunnelling plasmonics,” Nature 491(7425), 574–577 (2012). [CrossRef] [PubMed]
  44. R. A. de la Osa, J. M. Sanz, J. M. Saiz, F. González, F. Moreno, “Quantum optical response of metallic nanoparticles and dimers,” Opt. Lett. 37(23), 5015–5017 (2012). [CrossRef] [PubMed]
  45. W. A. Kraus, G. C. Schatz, “Plasmon resonance broadending in small metal particles,” J. Chem. Phys. 79(12), 6130–6139 (1983). [CrossRef]

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