Lorenz-Mie theory for 2D scattering and resonance calculations

This PhD tutorial is concerned with a description of the two-dimensional generalized Lorenz-Mie theory (2D-GLMT), a well-established numerical method used to compute the interaction of light with arrays of cylindrical scatterers. This theory is based on the method of separation of variables and the application of an addition theorem for cylindrical functions. The purpose of this tutorial is to assemble the practical tools necessary to implement the 2D-GLMT method for the computation of scattering by passive scatterers or of resonances in optically active media. The first part contains a derivation of the vector and scalar Helmholtz equations for 2D geometries, starting from Maxwell's equations. Optically active media are included in 2D-GLMT using a recent stationary formulation of the Maxwell-Bloch equations called steady-state ab initio laser theory (SALT), which introduces new classes of solutions useful for resonance computations. Following these preliminaries, a detailed description of 2D-GLMT is presented. The emphasis is placed on the derivation of beam-shape coefficients for scattering computations, as well as the computation of resonant modes using a combination of 2D-GLMT and SALT. The final section contains several numerical examples illustrating the full potential of 2D-GLMT for scattering and resonance computations. These examples, drawn from the literature, include the design of integrated polarization filters and the computation of optical modes of photonic crystal cavities and random lasers.Comment: This is an author-created, un-copyedited version of an article published in Journal of Optics. IOP Publishing Ltd is not responsible for any errors or omissions in this version of the manuscript or any version derived from i

Impurity-induced modulation of terahertz waves in optically excited GaAs

The effect of the photoinduced absorption of terahertz (THz) radiation in a semi-insulating GaAs crystal is studied by the pulsed THz transmission spectroscopy. We found that a broad-band modulation of THz radiation may be induced by a low-power optical excitation in the spectral range of the impurity absorption band in GaAs. The measured modulation achieves 80\%. The amplitude and frequency characteristics of the resulting THz modulator are critically dependent on the carrier density and relaxation dynamics in the conduction band of GaAs. In semi-insulating GaAs crystals, the carrier density created by the impurity excitation is controlled by the rate of their relaxation to the impurity centers. The relaxation rate and, consequently, the frequency characteristics of the modulator can be optimized by an appropriate choice of the impurities and their concentrations. The modulation parameters can be also controlled by the crystal temperature and by the power and photon energy of the optical excitation. These experiments pave the way to the low-power fast optically-controlled THz modulation, imaging, and beam steering.Comment: 5 pages, 3 figure

Controlling the localization and migration of optical excitation

In the nanoscale structure of a wide variety of material systems, a close juxtaposition of optically responsive components can lead to the absorption of light by one species producing fluorescence that is clearly attributable to another. The effect is generally evident in systems comprising two or more light-absorbing components (molecules, chromophores or quantum dots) with well-characterised fluorescence bands at similar, differentiable wavelengths. This enables the fluorescence associated with transferred energy to be discriminated against fluorescence from an initially excited component. The fundamental mechanism at the heart of the phenomenon, molecular (resonance) energy transfer, also operates in systems where the product of optical absorption is optical frequency up-conversion. In contrast to random media, structurally organised materials offer the possibility of pre-configured control over the delocalization of energy, through molecular energy transfer following optical excitation. The Förster mechanism that conveys energy between molecular-scale components is strongly sensitive to specific forms of correlation between the involved components, in terms of position, spectroscopic character, and orientation; one key factor is a spectroscopic gradient. Suitably designed materials offer a broad scope for the widespread exploitation of such features, in applications ranging from chemical and biological sensing to the detection of nanoscale motion or molecular conformations. Recently, attention has turned to the prospect of actively controlling the process of energy migration, for example by changing the relative efficiencies of fluorescence and molecular energy transfer. On application of static electric fields or off-resonant laser light - just two of the possibilities - each represents a means for achieving active control with ultrafast response, in suitably configured systems. As the principles are established and the theory is developed, a range of new possibilities for technical application is emerging. For example, applications can be envisaged for new forms of all-optical switching and transistor action. There is also interest in engaging with the interplay of optical excitation and local nanoscale force, exploiting local responses to changes in dispersion forces, accompanying molecular energy transfer

Optical activity in the Drude helix model

An old classical one-particle helix model for optical activity, first proposed by Drude, is reconsidered here. The quantum Drude model is very instructive because the optical activity can be calculated analytically without further approximations apart from the Rosenfeld long wavelength approximation. While it was generally believed that this model, when treated correctly, is optically inactive, we show that it leads to optical activity when the motion of the particle is quantum mechanically treated. We also find that optical activity arises even in the classical regime at non-zero energy, while for zero energy the model is inactive, in accordance with previous results. The model is compared with other one-electron models and it is shown that its predicted optical activity is qualitatively different from those of other one-electron systems. The vanishing of optical activity in the classical zero-energy limit for the Drude model is due to the localization of the particle at the equilibrium position, whereas in the analogous model of a particle moving freely on a helix without a definite equilibrium position, optical activity does not vanish but the spectrum is rescaled. The model under study leads to interesting predictions about the optical properties of e. g. helicene derivatives

Optical properties of cosmic dust analogs: A review

Nanometer- and micrometer-sized solid particles play an important role in the evolutionary cycle of stars and interstellar matter. The optical properties of cosmic grains determine the interaction of the radiation field with the solids, thereby regulating the temperature structure and spectral appearance of dusty regions. Radiation pressure on dust grains and their collisions with the gas atoms and molecules can drive powerful winds. The analysis of observed spectral features, especially in the infrared wavelength range, provides important information on grain size, composition and structure as well as temperature and spatial distribution of the material. The relevant optical data for interstellar, circumstellar, and protoplanetary grains can be obtained by measurements on cosmic dust analogs in the laboratory or can be calculated from grain models based on optical constants. Both approaches have made progress in the last years, triggered by the need to interpret increasingly detailed high-quality astronomical observations. The statistical theoretical approach, spectroscopic experiments at variable temperature and absorption spectroscopy of aerosol particulates play an important role for the successful application of the data in dust astrophysics.Comment: 18 pages, 6 figures, invited review for Journal of Nanophotonics, Special Section to honour C.F. Bohre