Diffraction and localization in low-dimensional photonic bandgaps

We show that, in low-dimensional photonic bandgaps, wave diffraction resulting from localization in the translational-invariant directions is strongly influenced by the photonic band structure of the periodic crystal, leading to new kinds of wave localization. In particular, for a periodic layered structure we show that, close to a bandgap edge, diffraction is enhanced, with a transition from a parabolic diffraction curve-typical of isotropic media and supporting Gaussian beams-to hyperbolic or elliptic diffraction curves. In the last two cases localization in the form of stationary X-shaped or sinc-shaped waves is possible.     

Algebraic aspects of crystallography

Taking into account the fact that space groups are groups of transformations of Euclideann-dimensional space, non-equivalent systems of non-primitive translations are defined. They can be brought into one-to-one correspondence with the elements of the groupH ¹ (K, R ⁿ /Z ⁿ ) or with those of the groupH ¹ (K, Z ⁿ /kZ ⁿ )/H ¹ (K, Z ⁿ ). (K is a point group of orderk.) The consistency of these findings with the results of Part I is given by the isomorphisms $$H^2 (K,Z^n ) \cong H^1 (K,R^n /Z^n ) \cong H^1 (K,Z^n /kZ^n )/H^1 (K,Z^n ).$$ Theorems are proved giving the conditions for cohomology groupsH ^q (K, A) to be zero. These conditions are fulfilled in particular ifA=R ⁿ andK is a subgroup ofGL (n, R) that either is compact (thenq>0) or has a finite normal subgroup leaving no element ofR ⁿ invariant (thenq≧0). This implies that the affine, the Euclidean and the inhomogeneous Lorentz groups are the only extensions ofR ⁿ by the corresponding homogeneous groups. By way of illustration, the theory of this paper is applied to two 2-dimensional space groups.     

Perturbed geodesics on the moduli space of flat connections and Yang–Mills theory

If we consider the moduli space of flat connections of a non trivial principal SO(3)-bundle over a surface, then we can define a map from the set of perturbed closed geodesics, below a given energy level, into families of perturbed Yang–Mills connections depending on a parameter ${\varepsilon}$ . In this paper we show that this map is a bijection and maps perturbed geodesics into perturbed Yang–Mills connections with the same Morse index.     

Elliptic Yang–Mills flow theory

We lay the foundations of a Morse homology on the space of connections on a principal G‐bundle over a compact manifold Y, based on a newly defined gauge‐invariant functional on . While the critical points of correspond to Yang–Mills connections on P, its L²‐gradient gives rise to a novel system of elliptic equations. This contrasts previous approaches to a study of the Yang–Mills functional via a parabolic gradient flow. We carry out the analytical details of our programme in the case of a compact two‐dimensional base manifold Y. We furthermore discuss its relation to the well‐developed parabolic Morse homology over closed surfaces. Finally, an application of our elliptic theory is given to three‐dimensional product manifolds .     

Observation of wave packet dichotomy and adiabatic stabilization in an optical waveguide

We report on the first experimental observation of wave packet dichotomy and adiabatic stabilization of light in a periodically bent optical waveguide in analogy with similar behavior of atoms in high-frequency strong laser fields.     

Demonstration of differential phase-shift keying demodulation at 10 Gbit/s optimal fiber Bragg grating filters

Optimal demodulation of differential phase-shift keying signals at 10 Gbit/s is experimentally demonstrated using a specially designed structured fiber Bragg grating composed by Fabry-Perot coupled cavities. Bit-error-rate measurements show that, as compared with a conventional Gaussian-shaped filter, our demodulator gives approximately 2.8 dB performance improvement.     

Separation of interface and bulk contributions in second-harmonic generation from magnetic and non-magnetic multilayers

We discuss the separation problem of bulk vs interface contributions in optical Second-Harmonic Generation (SHG). A new method is presented, which — in special cases — provides a full separation of all interface and bulk tensor components. The method is based on measurements in a thin-film geometry, and the relation between two bulk tensor components obtained from group-theoretical arguments. The separation problem in its strict sense is shown to be absent in Magnetization-induced SHG (MSHG). Though, in practice, also in the MSHG case interface and bulk contributions can be closely resemblant. The approach is illustrated by second-harmonic experiments on C₆₀ thin films. SHG in this system is found to be completely dominated by bulk processes.Paper presented at the 129th WE-Heraeus-Seminar on Surface Studies by Nonlinear Laser Spectroscopies, Kassel, Germany, May 30 to June 1, 1994