Knots, Symmetry, and Scattering

We investigate the physics underlying the scattering of circularly polarized plane waves from a toroidal knot and related unknot. We find that backscattering along the axis of rotational symmetry from trefoil knots is cross polarized; copolarized backscatter is in the numerical noise. In contrast, untrefoils give appreciable backscattering cross sections for both polarizations. We also study an intermediate class of structures: morphs, which provides a geometrical bridge between trefoil and untrefoil. We pursue physical insight for the depolarization associated with asymmetric objects, tracing the connection from the induced charge distribution, to the induced moments, to the polarization of the backscattered field

Higher-order Bragg coupling in periodic media with gain or loss

We consider wave propagation in longitudinally periodic media with gain or loss. An extended coupled-waves (ECW) approach and Floquet approach are used to study index and gain (or loss) coupling in periodic media at the first few Bragg resonances by the use of Brillouin diagrams. Phase speeding or slowing that is dependent upon the type of coupling occurs in periodic media. Even and odd resonances display different dispersion characteristics. Several examples of coupling due to multiharmonic periodicities are also covered. Coupling or feedback strength can be continuously varied by changing the relative phase of multiharmonic periodicities

Lacunarity of Fractal Superlattices: a Remote Estimation using Wavelets

The lacunarity provides a useful parameter for describing the distribution of gap sizes in discrete self-similar (fractal) superlattices and is used in addition to the similarity dimension to describe fractals. We show here that lacunarity, as well as the similarity dimension, can be remotely estimated from the wavelet analysis of superlattices impulse response. As a matter of fact, the skeleton—the set of wavelet-transform modulus-maxima—of the reflected signal overlaps two hierarchical structures in the time-scale domain: such that one allows the direct remote extraction of the similarity dimension, while the other may provide an accurate estimation of the lacunarity of the interrogated superlattice. Criteria for the choice of the mother wavelet are established for impulse response corrupted by additive Gaussian white noise

Transients in a periodic slab: Coupled waves approach

The reflection and transmission of rectangular and Gaussian pulses impinging on a periodically stratified slab are studied and a number of examples are illustrated and analyzed. The coupled waves approach is used to derive the reflection and transmission coefficient, then the fast Fourier transform is used to illustrate the transient responses

Canonical Sources and Duality in Chiral Media

Chiral media are characterized by the constitutive relations D = εE + iXicB and H = B/µ + iXicE where Xic is the chirality admittance introduced to take into account macroscopic handedness or optical activity inherent in the media. In addition we define a chirality impedance and a dimensionless chirality factor to describe the wave properties of this medium. As known for some time, this medium supports the plane-wave propagation of circularly polarized waves of opposing handedness and differing wavenumbers. Here we examine the radiation of electromagnetic waves from a set of simple canonical arrays. This leads us to the notion of duality for chiral media which can be exhibited in a surprisingly simple form. We show that in the far field, both point and extended sources, whether electric or magnetic, radiate two electromagnetic eigenmodes which are of opposing handedness. We also demonstrate sources which access only one of the eigenmodes of the medium. Several applications of the results and array performance in chiral media are noted

Synchronization Recovery of Chaotic Wave Through an Imperfect Channel

We present a novel idea to recover synchronization using the genetic algorithm after a chaotic wave passes through an imperfect channel with constant attenuation and offset. The compensation block, which is added before the receiver, is used to compensate the distortion of the imperfect channel. A new concept, the synchronization mismatch is defined and used as the cost function in genetic algorithm to design the compensation block. The validity of this approach is suggested by numerical simulations

Transients in a periodic slab: Coupled waves approach

The reflection and transmission of rectangular and Gaussian pulses impinging on a periodically stratified slab are studied and a number of examples are illustrated and analyzed. The coupled waves approach is used to derive the reflection and transmission coefficient, then the fast Fourier transform is used to illustrate the transient responses

Periodic Chiral Structures

The electromagnetic properties of a structure that is both chiral and periodic are investigated using coupled-mode equations. The chirality is characterized by the constitutive relations D = εE + iXicB and H = iXicE+B/µ, where Xic is the chiral admittance. The periodicity is described by a sinusoidal perturbation of the permittivity, permeability and chiral admittance. The coupled-mode equations are derived from physical considerations. The coupled-mode equations are used to examine bandgap structure and reflected and transmitted fields. Chirality is observed predominantly in transmission while periodicity is present in both reflection and transmission