Nonlinear parameter retrieval from three- and four-wave mixing in metamaterials

We present a generalized nonlinear susceptibility retrieval method for metamaterials based on transfer matrices and valid in the nondepleted pump approximation. We construct a general formalism to describe the transfer matrix method for nonlinear media and apply it to the processes of three- and four-wave mixing. The accuracy of this approach is verified via finite element simulations. The method is then reversed to give a set of equations for retrieving the nonlinear susceptibility. Finally, we apply the proposed retrieval operation to a three-wave mixing transmission experiment performed on a varactor loaded split ring resonator metamaterial sample and find quantitative agreement with an analytical effective medium theory model. © 2010 The American Physical Society.

Nonlinear oscillator metamaterial model: numerical and experimental verification.

We verify numerically and experimentally the accuracy of an analytical model used to derive the effective nonlinear susceptibilities of a varactor-loaded split ring resonator (VLSRR) magnetic medium. For the numerical validation, a nonlinear oscillator model for the effective magnetization of the metamaterial is applied in conjunction with Maxwell equations and the two sets of equations solved numerically in the time-domain. The computed second harmonic generation (SHG) from a slab of a nonlinear material is then compared with the analytical model. The computed SHG is in excellent agreement with that predicted by the analytical model, both in terms of magnitude and spectral characteristics. Moreover, experimental measurements of the power transmitted through a fabricated VLSRR metamaterial at several power levels are also in agreement with the model, illustrating that the effective medium techniques associated with metamaterials can accurately be transitioned to nonlinear systems.

Structural manifestation of the delocalization error of density functional approximations: C(4N+2) rings and C(20) bowl, cage, and ring isomers.

The ground state structure of C(4N+2) rings is believed to exhibit a geometric transition from angle alternation (N < or = 2) to bond alternation (N > 2). All previous density functional theory (DFT) studies on these molecules have failed to reproduce this behavior by predicting either that the transition occurs at too large a ring size, or that the transition leads to a higher symmetry cumulene. Employing the recently proposed perspective of delocalization error within DFT we rationalize this failure of common density functional approximations (DFAs) and present calculations with the rCAM-B3LYP exchange-correlation functional that show an angle-to-bond-alternation transition between C(10) and C(14). The behavior exemplified here manifests itself more generally as the well known tendency of DFAs to bias toward delocalized electron distributions as favored by Huckel aromaticity, of which the C(4N+2) rings provide a quintessential example. Additional examples are the relative energies of the C(20) bowl, cage, and ring isomers; we show that the results from functionals with minimal delocalization error are in good agreement with CCSD(T) results, in contrast to other commonly used DFAs. An unbiased DFT treatment of electron delocalization is a key for reliable prediction of relative stability and hence the structures of complex molecules where many structure stabilization mechanisms exist.

Mix it and fix it: functions of composite olfactory signals in ring-tailed lemurs.

Animals communicating via scent often deposit composite signals that incorporate odorants from multiple sources; however, the function of mixing chemical signals remains understudied. We tested both a 'multiple-messages' and a 'fixative' hypothesis of composite olfactory signalling, which, respectively, posit that mixing scents functions to increase information content or prolong signal longevity. Our subjects-adult, male ring-tailed lemurs (Lemur catta)-have a complex scent-marking repertoire, involving volatile antebrachial (A) secretions, deposited pure or after being mixed with a squalene-rich paste exuded from brachial (B) glands. Using behavioural bioassays, we examined recipient responses to odorants collected from conspecific strangers. We concurrently presented pure A, pure B and mixed A + B secretions, in fresh or decayed conditions. Lemurs preferentially responded to mixed over pure secretions, their interest increasing and shifting over time, from sniffing and countermarking fresh mixtures, to licking and countermarking decayed mixtures. Substituting synthetic squalene (S)-a well-known fixative-for B secretions did not replicate prior results: B secretions, which contain additional chemicals that probably encode salient information, were preferred over pure S. Whereas support for the 'multiple-messages' hypothesis underscores the unique contribution from each of an animal's various secretions, support for the 'fixative' hypothesis highlights the synergistic benefits of composite signals.