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Optics Express

Optics Express

  • Editor: C. Martijin de Sterke
  • Vol. 15, Iss. 9 — Apr. 30, 2007
  • pp: 5730–5741
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A quantum chemical approach to the design of chiral negative index materials

Alexander Baev, Marek Samoc, Paras N. Prasad, Mykhaylo Krykunov, and Jochen Autschbach  »View Author Affiliations


Optics Express, Vol. 15, Issue 9, pp. 5730-5741 (2007)
http://dx.doi.org/10.1364/OE.15.005730


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Abstract

This paper presents methodology developed for the computational modeling and design of negative refractive index materials (NIMs) based on molecular chirality. An application of the methodology is illustrated by ab initio computations on two organometallic molecules which constitute the monomer units of a chiral polymer. Comparisons with experimental data for the polymer are made. Even though the resulting chirality parameter for the pristine material is small, it is shown that negative index can be achieved by introducing sharp plasmonic resonances with metal nanoparticle inclusions.

© 2007 Optical Society of America

1. Introduction

There is a tremendous interest in the possibility of development of materials and structures (metamaterials) with the ability to exhibit a negative index of refraction [1]. Various approaches have been proposed to achieve the negative index within an electromagnetic wavelength range of interest, with the highest interest in the materials for the visible-infrared range. There are a number of technological challenges that are difficult to meet with typical metamaterial approaches. The optical losses of the medium have to be manageable to provide for effects such as focusing by plane-parallel negative index material (NIM) slabs [2

2. J. B. Pendry, “Negative refraction makes a perfect lens,” Phys. Rev. Lett. 85, 3966–3969 (2000). [CrossRef] [PubMed]

]. It would also be advantageous if the negative index could be obtained over a range of directions for propagation of light. One of the proposed routes towards negative refractive indices is based on the use of strongly chiral media [3–10

3. S. Tretyakov, I. Nefedov, A. Sihvola, S. Maslovski, and C. Simovski, “Waves and energy in chiral nihility,” J. Electromagn. Waves Appl. 17, 695–706 (2003). [CrossRef]

]. This may potentially lead to materials for which some of the problems encountered with metamaterials are alleviated. In particular, neither permittivity nor permeability needs to be negative to achieve NIM in this approach. Moreover, the difficulty of the NIM paradigm is avoided of extending the concept of a magnetic resonance to the frequency region corresponding to the visible range. Electrical and magnetic properties in the resonant region are treated within the same framework of quantum chemical simulations. The new paradigm calls for the use of chiral molecules or chiral supramolecular and polymeric structures. By using such a “chemical” approach, it is possible to reduce the need for including metamaterial components with dimensions comparable to the wavelength of light, and to use smaller active elements than in the typical metamaterial approach, which would help to reduce scattering losses. In this paper we investigate a quantum chemical protocol for the design and optimization of molecular structures suitable as building blocks for negative refractive index (meta) materials.

2. Methodology

In a chiral medium, i.e. in a medium exhibiting electromagnetic handedness, an electric or magnetic excitation simultaneously produces both electric and magnetic polarization. The background of our approach stems from the so-called bi-isotropic formulation of the constitutive relations proposed by Condon in his early 1937 paper [11

11. E. U. Condon, “Theories of optical rotatory power,” Rev. Mod. Phys. 9, 432–457 (1937). [CrossRef]

]. This formulation of the constitutive relations assumes a reciprocally bi-isotropic chiral medium. The sought-after material is indeed isotropic because we assume a non-ordered random distribution of chiral structures inside, for example, a host matrix, with λ≫a, where λ is the wavelength of the incident light and a is a characteristic size of the material’s constituents. It is also reciprocal because it is assumed linear and non-magnetic (i.e. a magneto-electric effect does not occur). Finally, the bulk material is chiral as consisting of chiral molecules. The bi-isotropic constitutive relations are given as

Dˉ=εEˉ+(χ)ε0μ0Hˉ,
Bˉ=μHˉ+(χ+)ε0μ0Eˉ
(1)

in SI units, where χ is the non-reciprocity parameter and κ is the chirality parameter. Evidently, χ = 0 for a reciprocal material. Negative refraction (or backward waves) will occur at one of the eigen (circular) polarizations of the incident light, if the chirality parameter, κ, is larger than the square root of the product of permittivity and permeability [3

3. S. Tretyakov, I. Nefedov, A. Sihvola, S. Maslovski, and C. Simovski, “Waves and energy in chiral nihility,” J. Electromagn. Waves Appl. 17, 695–706 (2003). [CrossRef]

]:

k±=k0(εμ±κ).
(2)

Here, k ± is the propagation constant of two eigen-waves in the isotropic chiral medium, κ is the chirality parameter, ε denotes the scalar macroscopic dielectric permittivity (for an isotropic material), and μ denotes the macroscopic magnetic permeability.

Development of methods for the ab initio theoretical modeling of chiral NIMs is of great significance as it can provide a basis to understand the structure-property relations necessary for a rational design of the material’s building blocks. In turn, this can lead to an optimization of structures for producing molecular materials with large chiral parameters. It is worthwhile to note that in the area of computational nanophotonics density functional theory (DFT) is usually preferred to wavefunction based ab initio calculations. This is because DFT combines affordable computational costs and reasonably high accuracy due to effects from electron correlation. We present in this paper a framework to study NIMs which utilizes first principles quantum chemical computations of the mixed electric-magnetic polarizabilities that are responsible for chiral properties of molecules. In this quantum-theoretical approach we start out by building the basic building blocks of the material from atomic nuclei and electrons and express the whole system in terms of the Schrödinger or Dirac equations. These equations can only be solved after using a series of approximations based on the underlying physics and mathematics. The property of interest is then obtained by applying time-dependent variational density-functional response theory to calculate the linear response functions with respect to electric and magnetic dipole fields [12

12. K. Ruud and T. Helgaker, “Optical rotation studied by density-functional and coupled-cluster methods,” Chem. Phys. Lett. 352, 533–539 (2002). [CrossRef]

, 19–21

19. M. Krykunov and J. Autschbach, “Calculation of origin independent optical rotation tensor components for chiral oriented systems in approximate time-dependent density functional theory,” J. Chem. Phys. 125, 034102-10 (2006). [CrossRef]

]. These have now been coded for the calculation of most electromagnetic properties, resonant or non-resonant, representing low or high orders in the matter-field interaction, including the electromagnetic linear or nonlinear chirality properties of interest. Theoretical modeling can fulfill two important tasks: to predict the chirality of a given material on the molecular level and to establish structure-property relations that can assist the chemical synthesis of new materials with the desired functionality. To find a molecule with the highest possible value of molecular chirality, it would be desirable to preliminarily analyze the possible outcome before starting time-consuming ab initio calculations. Such an analysis may be based on analytical models [13

13. J. J. Maki and A. Persoons, “One-electron second-order optical activity of a helix,” J. Chem. Phys. 104, 9340 (1996). [CrossRef]

, 14

14. S. A. Tretyakov, F. Mariotte, C. R. Simovski, T. G. Kharina, and J.-P. Heliot, “Analytical antenna model for chiral scatterers: Comparison with numerical and experimental data,” IEEE Trans. Antennas Propag. 44, 1006 (1996). [CrossRef]

] of electric dipole-magnetic dipole polarizability of a small particle. Though classical in nature, for a helical molecule these models might yield the same scaling law with pitch and radius of the helix as in the quantum mechanical calculations. This would allow for identifying promising candidates for refined ab initio computations simply by inspecting an optimized geometry (which can be obtained with fast semi-empirical methods, such as AM1 or PM3). A higher value of the ratio of radius to pitch should be expected to indicate an increase in the value of the optical rotatory parameter, in particular when comparing systems that have similar chromophores (meant here as highly polarizable moieties). Other criteria are also of importance. For molecules with chains containing delocalized π-electrons such a criterion is the conjugation length, which influences the magnitude of the molecular polarizability. This and other issues have to be addressed in the design process. We envision that simple models may be used for a fast screening of a large set of potential compounds. However, follow-up ab initio computations need to confirm if the system has a large chirality parameter since the relation between structure and optical activity is complex and influenced by many factors such as functional groups, the exact nature of the chromophore and so on.

Fig. 1. Monomeric Ni complex 1. Right: monomer unit of the polymer. Left: model complex used in the ab-initio computations to represent the monomer.

Once a promising structure is chosen, the quantum chemical ab initio computations can be applied to determine the microscopic molecular chirality as well as the polarizability. Various approaches can then be used to assess the macroscopic dielectric properties of a medium composed of chiral molecules. In the simplest case one can assume an oriented gas without interactions between the molecules that constitute the components of the material. Composite materials can be dealt with through an effective medium (EM) approach, for instance the Maxwell-Garnett mixing formula. Within this approach one can also assess the influence of modifications in the local fields encountered by the chiral molecule on the macroscopic chirality parameter. One possible way of obtaining very large chirality parameters is the so-called supramolecular approach where self-assembling helical structures of chiral molecules boost the chirality [15

15. V. Percec, M. Glodde, T. K. Bera, Y. Miura, I. Shiyanovskaya, K. D. Singer, V. S. K. Balagurusamy, P. A. Heiney, I. Schnell, A. Rapp, H. W. Spiess, S. D. Hudson, and H. Duan, “Self-organization of supramolecular helical dendrimers into complex electronic materials,” Nature 419, 384–387 (2002). [CrossRef] [PubMed]

]. Such an approach may, however, require a more refined theoretical methodology for computation of the chirality since ab initio computations of the optical activity of supramolecular assemblies are far from being straightforward. However, we envision that ab initio computations may be instrumental even for macromolecules in this framework. For instance they may be utilized to determine the transition dipole moments of the electronic excitations for the monomer structures and the influence of coupling between a few oligomer units. Based on this and some basic structural information, a coupling model should be able to yield a reliable estimate of the chirality parameter near a resonance. For wavelengths far away from resonances direct computations of the optical rotatory strength for the monomer and small oligomer units might yield useful insight.

In the following we illustrate how quantum chemistry derived data can be used to predict properties of a model chiral material. We employ here computations carried out on two chiral organometallic complexes. The complexes are not yet optimized for high chirality but are representative of relatively small chiral molecules with comparatively strong optical activity. The computed values can be compared to a set of preliminary experimental data that we have obtained from circular dichroism studies. The complexes are shown in Figs. 1 and 2.

Fig. 2. Monomeric Co complex 2

3. Estimation of the chirality parameter from an experimental CD spectrum

κ=Nμ0βωc,
(3)

φ=13ω2(n2+2)Nμ0β,
(4)

where φ is in [rad/m] and n is the refractive index of the medium. The (n 2 + 2)/3 factor in the last equation may be determined in the ab initio (see below) computations by considering medium effects on β directly, for instance by employing a continuum model. For the purpose of this initial study we have neglected medium effects in the computations.

In Fig. 3 we show the measured molar ellipticity in conventional units of [deg cm2/dmol] and the ORD obtained from a numerical Kramers-Kronig transformation of the CD spectrum. Further, we show the corresponding dispersion of the chirality parameter, κ, for the dilute solution used for the measurements. As one can see, the chirality parameter is extremely small, even in the resonant region. The magnitude of κ can readily be increased by about 5 orders of magnitude by using a bulk solid of the chiral polymer instead of a dilute solution. In the solid the concentration of the chiral molecules would be on the order of 1 – 10 M. However, even in the case of a medium composed entirely of the chiral Ni complex polymer the chirality parameter would still be on the order of 10-3 which is significantly lower than what is needed to achieve a negative refractive index in the off-resonant frequency range. This prompts for a modeling and design of molecular structures with significantly higher chirality.

Fig. 3. (a). Dispersion of molar ellipticity (experimental data) and molar rotation (KK transform of CD spectrum), and (b) chirality parameter of the Ni complex 1

4. Estimation of the chirality parameter by means of ab initio calculations

Having an experimental estimate for the magnitude of the chirality parameter, we now embark on theoretical modeling of the chiroptical properties to assess the fidelity of the quantum chemical approach. The chirality parameter can be estimated through Eq. (3), taking the values of β computed ab initio according to

β=1ω(Gxx+Gyy+Gzz)3,
(5)

where Gii are the diagonal elements of the gyration tensor (mixed electric-magnetic dipole polarizability) which is formally defined as

Gαβωω=2ħn0ωωn02ω2m(0μ̂αnnm̂β0).
(6)

Here μ^ and are electric dipole and magnetic dipole moment operators, respectively. It is worthwhile to note here that the trace of gyration tensor is gauge origin independent which makes it the only observable quantity for a chiral isotropic medium (solution of chiral molecules). In order to obtain origin-independent optical rotation tensor elements it is necessary to include an electric quadrupole term in addition to G′ [18

18. A. D. Buckingham and M. B. Dunn, “Optical activity of oriented molecules,” J. Chem. Soc. A 1988 (1971).

,19

19. M. Krykunov and J. Autschbach, “Calculation of origin independent optical rotation tensor components for chiral oriented systems in approximate time-dependent density functional theory,” J. Chem. Phys. 125, 034102-10 (2006). [CrossRef]

]. We point out that the optical rotatory parameter is not calculated explicitly from a summation as in Eq. (6) but from a linear response function derived specifically for the time-dependent density-functional theory (TDDFT) approach that was used for this study [20

20. J. Autschbach and T. Ziegler, “Calculating electric and magnetic properties from time dependent density functional perturbation theory,” J. Chem. Phys. 116, 891–896 (2002). [CrossRef]

, 21

21. J. Autschbach, T. Ziegler, S. Patchkovskii, S. J. A.van Gisbergen, and E. J. Baerends, “Chiroptical properties from time-dependent density functional theory. II. Optical rotations of small to medium sized organic molecules,” J. Chem. Phys. 117, 581–592 (2002). [CrossRef]

]. In this approach all excitations possible within the given finite basis set are implicitly included in the calculation of β.

Table I. Dispersion of electric polarizability, magnetizability, and optical rotatory parameter for Ni complex 1

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Table II. Dispersion of optical rotatory parameter for Co complex 2

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The results of our ab initio calculations are depicted in Fig. 4. The concentration of chiral molecules was set to 4.4 ×10-6 M in order to compare directly with the experiment. The comparison is obviously somewhat limited in scope because the experimental data have been obtained for a polymer whereas the computation was performed on the monomer unit. Nonetheless, the theoretical data should give a rough estimate of the chirality parameter to be expected as long as the monomer units in the polymer do not couple too strongly. This does not seem to be the case since the theoretically computed κ is of the same order of magnitude as the one computed from the experimental CD spectrum (see Figs. 3 and 4). As already mentioned, the low absolute value of the chirality parameter is in part due to the low concentration of chiral species in solution.

Fig. 4. Theoretical chirality parameter for Ni complex 1

One needs to mention here that in case of the bulk material with a very high number density of the constituent entities, the effective chirality parameter of the medium may need to be computed with a more realistic model for the local field effects. However, the increase of concentration alone will not yield a chirality parameter that is large enough to achieve negative refraction in a system built of relatively simple molecules like those considered here. As mentioned before, one scheme to achieve amplification of chirality is through supramolecular assembly of chiral units in helical form.

5. Tuning the effective refractive index of the chiral medium by applying plasmonic inclusions

One can envisage a situation where the dielectric function of a material is modified by adding to the chiral matrix another component which provides for a local suppression of the dielectric constant. One such possibility is through introducing plasmonic inclusions, such as metal nanoparticles. This can lower the real part of dielectric permittivity of the composite material, thereby providing the so-called “chiral nihility”, and even help in suppressing the imaginary part of the permittivity, thus overcoming resonant loss. We should note here that “chiral nihility” condition can in principle be realized in general bi-isotropic non-reciprocal (Tellegen) media or gyrotropic chiral media without any additional inclusions. However, this would only arise when the non-reciprocity parameter is large or when diagonal and off-diagonal components of the permittivity tensor cancel each other. These situations are analysed in much detail in Refs. 6 and 7 and will therefore not be discussed further in this work. According to [25

25. W. T. Doyle, “Optical properties of a suspension of metal spheres,” Phys. Rev. B 39, 9852–9858 (1989). [CrossRef]

], the effective dielectric permittivity of a medium composed of spherical particles embedded into a host matrix can be computed as follows:

εeff=εhostx33ifT1Ex3+3ifT1E2,
(7)

where x = 2πa /λ is the sphere size parameter, a is the radius of the sphere, λ is the wave length in the host medium, f is the volume fraction of nanoparticles, and TE 1 is the electric-dipole component of the scattering T-matrix in Mie approximation.

Fig. 5. Material parameters of composite medium when electromagnetic coupling between chiral molecules and nanospheres is neglected: (a) Chirality parameter, (b) Effective dielectric permittivity, (c) Effective index of refraction.

If electromagnetic coupling between chiral species and plasmonic nanoinclusions is accounted for in a manner described in Ref. [26

26. S. Tretyakov, A. Sihvola, and L. Jylhä, “Backward-wave regime and negative refraction in chiral composites,” arXiv:cond-mat/0509287, 1 (2005).

], the effective chirality parameter of the composite material acquires an additional resonance at 533 nm (Fig. 6). The resonance of the effective permittivity is also blue-shifted. A negative refractive index is obtained for a different sense of the circular polarization compared to the case without coupling, because now the effective chirality parameter is negative. The absorption loss is lower in this case because of the lower imaginary part of the effective permittivity (Fig. 6). The optimum volume fraction of nanoparticles in this case equals 0.027. It is worthwhile to note here that introducing EM coupling results not only in the blue shift of the resonant effective material parameters, but also in a much lower volume fraction of nanoparticles needed to obtain the NIM behavior.

Fig. 6. Material parameters of composite medium when electromagnetic coupling between chiral molecules and nanospheres is accounted for: (a) Chirality parameter, (b) Effective dielectric permittivity, (c) Effective index of refraction.

6. Discussion

In order to be consistent with the proposed methodology of the quest for the prospective NIMs, we analyzed the optimized geometries of both organo-metallic complexes with respect to the radius-to-pitch ratio, a/ζ (see Figs. 1 and 2). The value of this useful estimative quantity is 0.809 for Co complex and 0.821 for Ni complex. Such a simple estimate does indeed carry some information about the strength of optical rotation and may cautiously be used if rigorous quantum chemical calculations of polarizabilities are not feasible for some reasons. If one is interested in absolute value of the optical rotatory strength, the proportionality factor for a family of compounds must be computed along with the radius-to-pitch ratio [14

14. S. A. Tretyakov, F. Mariotte, C. R. Simovski, T. G. Kharina, and J.-P. Heliot, “Analytical antenna model for chiral scatterers: Comparison with numerical and experimental data,” IEEE Trans. Antennas Propag. 44, 1006 (1996). [CrossRef]

].

The central part of the problem pertaining to realization of NIMs is obviously the loss. Introducing plasmonic nanoinclusions with concentration much lower, than that of the chiral molecules, allows for shifting the resonance of the composite material to a frequency range, where the loss of the chiral constituent is lower. On the other hand there is also the additional loss due to plasmonic resonance. Consequently the latter needs to be smaller in magnitude, than the resonant loss of the chiral host matrix which is presumably achievable with the low concentration of nanoparticles. Making use of core-shell nanoparticles can give additional flexibility when it comes to tuning plasmonic resonances. It is worthwhile to mention at this point the sharpness of the plasmonic resonances (see Figs. 5 and 6). One may argue that such sharp resonances are not likely to be encountered in practice because of several factors e.g. the dispersion in sizes of the plasmonic nanoparticles. However, the need for sharpness of a resonance will be alleviated as stronger molecular chirality is achieved.

As regarding the ab initio modeling, there are a number of potential shortcomings arising from the approximations that need to be applied in order to keep the computational effort manageable. For instance, the TDDFT modeling of excitation spectra, CD spectra, and optical rotation is influenced by truncation of the basis set, by approximations in the density functionals, by neglecting or an approximate treatment of the molecule’s chemical environment, or the neglect of vibrational corrections [27

27. J. Autschbach, “Density Functional Theory applied to calculating optical and spectroscopic properties of metal complexes: NMR and Optical Activity,” Coord. Chem. Rev., in press.

]. In principle, these obstacles can be overcome at the expense of computational resources (CPU time and memory). From the comparison of the chirality parameter calculated for a monomer solution with the experimentally derived data we see that the agreement is reasonable for wavelengths below about 600 nm. It appears that the computed excitation energies are somewhat red shifted which, by virtue of the KK relations, rationalizes to some degree the overestimation of κ in the computations. In the long-wavelength regime perfect agreement between the computed chirality parameter and the data derived from experiment should not be expected. The reason lies in the fact that the experimental chirality parameter has been obtained from a numerical KK transformation of the CD spectrum, with the concomitant truncation errors from the finite range of integration. Two of us have shown previously [16

16. M. Krykunov, M. D. Kundrat, and J. Autschbach, “Calculation of circular dichroism spectra from optical rotatory dispersion, and vice versa, as complementary tools for theoretical studies of optical activity using time-dependent density functional theory,” J. Chem. Phys. 125, 194110-13 (2006). [CrossRef]

] that such truncation errors can be significant in the long-wavelength limit whereas a good quality resonant ORD can be obtained by using KK transformations over a finite wavelength range.

7. Conclusions

A methodology allowing for rational design of chiral materials possessing negative index of refraction and based on quantum chemical ab initio calculations of corresponding microscopic polarizabilities is presented. Realization of such a negative refractive index material is shown to be feasible provided molecular entity with high optical activity is synthesized. Plasmonic inclusions are demonstrated to be able to locally lower the real part of dielectric permittivity of a composite material thereby ensuring conditions of chiral nihility within a very narrow frequency range. The need for a three orders of magnitude increase in the value of the macroscopic chirality parameter to obtain a material in which a negative refractive index might be obtainable may be alleviated by the use of inclusions providing sharp resonances. Concomitant use of supramolecular self-assemblies and metal nanoparticles may be a viable pathway to obtaining isotropic negative refractive index materials.

Acknowledgments

The authors are grateful to E. Furlani for valuable discussions. This work was in part supported by a grant from the office of vice-President for Research at the University at Buffalo and in part by the Chemistry and Life Sciences Directorate of the Air Force office of Scientific Research.

References and links

1.

A. N. Grigorenko, “Negative refractive index in artificial metamaterials,” Opt. Lett. 31, 2483–2485 (2006). [CrossRef] [PubMed]

2.

J. B. Pendry, “Negative refraction makes a perfect lens,” Phys. Rev. Lett. 85, 3966–3969 (2000). [CrossRef] [PubMed]

3.

S. Tretyakov, I. Nefedov, A. Sihvola, S. Maslovski, and C. Simovski, “Waves and energy in chiral nihility,” J. Electromagn. Waves Appl. 17, 695–706 (2003). [CrossRef]

4.

J. B. Pendry, “A chiral route to negative refraction,” Science 306, 1353–1355 (2004). [CrossRef] [PubMed]

5.

Y. Jin and S. He, “Focusing by a slab of chiral medium,” Opt. Express 13, 4974–4979 (2005). [CrossRef] [PubMed]

6.

J. Q. Shen and S. He, “Backward waves and negative refractive indices in gyrotropic chiral media,” J. Phys. A: Math. Gen. 39, 457–466 (2006). [CrossRef]

7.

J. Q. Shen, M. Norgren, and S. He, “Negative refraction and quantum vacuum effects in gyroelectric chiral mnedium and anisotropic magnetoelectric material,” Ann. Phys. (Leipzig) 15, 894–910 (2006). [CrossRef]

8.

V. M. Agranovich, Yu. N. Gartstein, and A. A. Zakhidov, “Negative refraction in gyrotropic media,” Phys. Rev. B 73, 045114 (2006). [CrossRef]

9.

Q. Cheng and T. J. Cui, “Negative refractions in uniaxially anisotropic chiral media,” Phys. Rev. B 73, 113104 (2006). [CrossRef]

10.

V. Yannopapas, “Negative index of refraction in artificial chiral materials,” J. Phys.: Condens. Matter 18, 6883–6890 (2006). [CrossRef]

11.

E. U. Condon, “Theories of optical rotatory power,” Rev. Mod. Phys. 9, 432–457 (1937). [CrossRef]

12.

K. Ruud and T. Helgaker, “Optical rotation studied by density-functional and coupled-cluster methods,” Chem. Phys. Lett. 352, 533–539 (2002). [CrossRef]

13.

J. J. Maki and A. Persoons, “One-electron second-order optical activity of a helix,” J. Chem. Phys. 104, 9340 (1996). [CrossRef]

14.

S. A. Tretyakov, F. Mariotte, C. R. Simovski, T. G. Kharina, and J.-P. Heliot, “Analytical antenna model for chiral scatterers: Comparison with numerical and experimental data,” IEEE Trans. Antennas Propag. 44, 1006 (1996). [CrossRef]

15.

V. Percec, M. Glodde, T. K. Bera, Y. Miura, I. Shiyanovskaya, K. D. Singer, V. S. K. Balagurusamy, P. A. Heiney, I. Schnell, A. Rapp, H. W. Spiess, S. D. Hudson, and H. Duan, “Self-organization of supramolecular helical dendrimers into complex electronic materials,” Nature 419, 384–387 (2002). [CrossRef] [PubMed]

16.

M. Krykunov, M. D. Kundrat, and J. Autschbach, “Calculation of circular dichroism spectra from optical rotatory dispersion, and vice versa, as complementary tools for theoretical studies of optical activity using time-dependent density functional theory,” J. Chem. Phys. 125, 194110-13 (2006). [CrossRef]

17.

C. R. Jeggo, “Nonlinear optics and optical activity,” J. Phys. C: Solid State Physics 5, 330–337 (1972). [CrossRef]

18.

A. D. Buckingham and M. B. Dunn, “Optical activity of oriented molecules,” J. Chem. Soc. A 1988 (1971).

19.

M. Krykunov and J. Autschbach, “Calculation of origin independent optical rotation tensor components for chiral oriented systems in approximate time-dependent density functional theory,” J. Chem. Phys. 125, 034102-10 (2006). [CrossRef]

20.

J. Autschbach and T. Ziegler, “Calculating electric and magnetic properties from time dependent density functional perturbation theory,” J. Chem. Phys. 116, 891–896 (2002). [CrossRef]

21.

J. Autschbach, T. Ziegler, S. Patchkovskii, S. J. A.van Gisbergen, and E. J. Baerends, “Chiroptical properties from time-dependent density functional theory. II. Optical rotations of small to medium sized organic molecules,” J. Chem. Phys. 117, 581–592 (2002). [CrossRef]

22.

E. J. Baerends et al., Amsterdam density functional, Theoretical Chemistry, Vrije Universiteit, Amsterdam (URL http://www.scm.com)

23.

M. Krykunov and J. Autschbach, “Calculation of optical rotation with time-periodic magnetic field-dependent basis functions in approximate time-dependent density functional theory,” J. Chem. Phys. 123, 114103-10 (2005). [CrossRef]

24.

J. Autschbach, L. Jensen, G. C. Schatz, Y. C. E. Tse, and M. Krykunov, “Time-dependent density functional calculations of optical rotatory dispersion including resonance wavelengths as a potentially useful tool for determining absolute configurations of chiral molecules,” J. Phys. Chem. A 110, 2461–2473 (2006). [CrossRef] [PubMed]

25.

W. T. Doyle, “Optical properties of a suspension of metal spheres,” Phys. Rev. B 39, 9852–9858 (1989). [CrossRef]

26.

S. Tretyakov, A. Sihvola, and L. Jylhä, “Backward-wave regime and negative refraction in chiral composites,” arXiv:cond-mat/0509287, 1 (2005).

27.

J. Autschbach, “Density Functional Theory applied to calculating optical and spectroscopic properties of metal complexes: NMR and Optical Activity,” Coord. Chem. Rev., in press.

OCIS Codes
(160.5470) Materials : Polymers

ToC Category:
Metamaterials

History
Original Manuscript: January 5, 2007
Revised Manuscript: April 17, 2007
Manuscript Accepted: April 17, 2007
Published: April 25, 2007

Citation
Alexander Baev, Marek Samoc, Paras N. Prasad, Mykhaylo Krykunov, and Jochen Autschbach, "A quantum chemical approach to the design of chiral negative index materials," Opt. Express 15, 5730-5741 (2007)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-15-9-5730


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References

  1. A. N. Grigorenko, "Negative refractive index in artificial metamaterials," Opt. Lett. 31, 2483-2485 (2006). [CrossRef] [PubMed]
  2. J. B. Pendry, "Negative refraction makes a perfect lens," Phys. Rev. Lett. 85, 3966-3969 (2000). [CrossRef] [PubMed]
  3. S. Tretyakov, I. Nefedov, A. Sihvola, S. Maslovski, and C. Simovski, "Waves and energy in chiral nihility," J. Electromagn. Waves Appl. 17, 695-706 (2003). [CrossRef]
  4. J. B. Pendry, "A chiral route to negative refraction," Science 306, 1353-1355 (2004). [CrossRef] [PubMed]
  5. Y. Jin and S. He, "Focusing by a slab of chiral medium," Opt. Express 13, 4974-4979 (2005). [CrossRef] [PubMed]
  6. J. Q. Shen and S. He, "Backward waves and negative refractive indices in gyrotropic chiral media," J. Phys. A: Math. Gen. 39, 457-466 (2006). [CrossRef]
  7. J. Q. Shen, M. Norgren, and S. He, "Negative refraction and quantum vacuum effects in gyroelectric chiral mnedium and anisotropic magnetoelectric material," Ann. Phys. (Leipzig) 15, 894-910 (2006). [CrossRef]
  8. V. M. Agranovich, Yu. N. Gartstein, and A. A. Zakhidov, "Negative refraction in gyrotropic media," Phys. Rev. B 73, 045114 (2006). [CrossRef]
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