Compendium on Electromagnetic Analysis

The following sections are included:

• Foreword
• Preface from the Editor-in-Chief
• Preface from the Editor
• About the Editor-in-Chief
• About the Editor
• Contents

In this chapter, we address some typical questions for those who study Raman scattering: What is the difference between infrared absorption and Raman spectroscopy? What is the reason for a vibrational mode to be infrared active and forbidden in Raman scattering spectra? Why is the Raman cross-section low? What is the mechanism of mixing between enhanced resonance Raman scattering and fluorescence? Finally, we present an example of biomolecule application.

This chapter covers the recent advances in fiber lasers with a distributed feedback (DFB). Being distinct from the ordinary lasers with fixed mirrors, DFB entails long reflection intervals that form an effective cavity. Experiments with passive and active fibers with regular and random mirrors are presented, including π-shifted gratings inscribed by femtosecond pulses. The results are preceded by theoretical background on Bragg reflectors and gratings with the π-shift. If amplification is present in an active fiber, the coupled wave equations become nonlinear. The corresponding linear and nonlinear equations are derived, and some of their exact solutions are considered in this chapter. The methods for solving the inverse scattering problem for the design of Bragg filter with a desired reflection spectrum are discussed. The fiber lasers are finding ever-widening applications in optical communications, sensor technology, and scientific research.

Nanoscale metallic particles interact strongly with electromagnetic fields through the excitation of localized surface plasmon resonances (LSPRs). This chapter introduces the concept of LSPRs supported by isolated particles and explores the roles played by composition, shape, and environment in determining their optical properties. In particular, classical, analytic models are introduced to describe the multipolar resonant modes for spheres of arbitrary size. Various approximations are then discussed, which provide a clear picture of the resonant properties of dipole responses for small particles, including those with non-spherical shapes. Finally, the strong field localization and enhancement associated with plasmonic excitation are discussed with a focus on the role played by multipole resonant modes and sharp geometric features. The subject of localized plasmon resonances is highly interdisciplinary, and it is our hope that the topics covered in this chapter will provide a broad overview of the foundational building blocks of plasmonic systems and their utility in scientific and technological applications.

We start by rapidly reviewing the elementary Drude model of conductors and show that it predicts large-scale collective oscillations of the “plasma” of conduction charge carriers in the volume of a conducting medium, often referred to as bulk plasmons. We then introduce the decomposition of fields into their longitudinal and transverse components and show that the bulk plasmons are longitudinal excitations with a characteristic plasmon frequency ω_L. A major physical result that ensues is that bulk transverse modes (i.e., radiative polaritons) do not exist below the longitudinal plasma frequency. We then proceed to discuss the physical significance of transient modes in lossy systems and the role played by causality. Next, we present the impedance/admittance methods that allow one to readily find and characterize the transient modes of semi-infinite conducting media possessing a planar (possibly, multi-layer) interface with a dielectric superstrate. The impedance method is used to find and characterize both the radiative polariton modes and the bound surface plasmon polariton modes of Drude-type conductors and to obtain some theoretical developments on energy conservation in multi-layer interfaces. Finally, we demonstrate that the methods introduced in this chapter provide a convenient means for understanding and characterizing the experimental applications that employ the prevalent Otto and Kretschmann configurations for coupling incident propagating light to surface plasmon polariton (SPP) excitations.

We consider plasmonic nanoantennae immersed in an active host medium. The metal nanoantennae can exhibit strong field enhancement in the optical spectral range due to the excitation of the plasmon resonance. Lasing in the metamaterial comprising such nanoantennae is considered. We show that the high losses predicted for the optical materials can be compensated in the gain medium. Gain allows us to achieve local generation in active metamaterials. We discuss plasmonic nanolasers where the metal nanoantenna operates in a fashion similar to an optical resonator. The size of the proposed plasmonic laser could be smaller than the wavelength of light. Therefore, it can serve as a very compact source of the coherent electromagnetic radiation and can be incorporated in future plasmonic devices.

In the presence of a plasmonic laser, the quantum effects in the plasmon EM field could be important. Quantum mechanical and thermal phenomena in the plasmonic nanoparticle are considered. The quantum plasmonics is developed by quantizing the collective electron motion. Thus, the obtained operator of the electric field inside the plasmonic nanoparticle is anomalously large so that the quantum electric field is comparable with the atomic field. The strong electric field results in huge electric current and thermal instability. We predict the thermal explosion of the metal nanoparticles when only few plasmons are excited.

Recent advances in nanofabrication have made possible the design and realization of large-area regular one-dimensional and two-dimensional metal nanoparticle arrays. These arrays exhibit far-field coupling of localized plasmons resulting in the so-called surface lattice resonances (SLRs) (also known as diffraction coupled localized plasmon resonances). SLRs possess a number of useful properties such as a high level of tunability and remarkably narrow linewidths. Here, we briefly outline the theory and experimental realization of SLRs. We then discuss applications of SLRs in sensing, light emission and absorption, hybrid systems with two-dimensional materials and solar energy conversion.

This chapter aims to highlight the contribution of the toroidal multipoles, particularly the dipole, in the multipole expansion analysis. The toroidal dipole is a peculiar excitation that differs from the familiar electric and magnetic multipoles, which involve the time-dependent separation of negative and positive charges and the closed circulation of electric currents, respectively. The toroidal dipole arises from the poloidal currents circulating on a surface of a gedanken torus along its meridians. Due to its low intensity, its role has been overshadowed by the usually much stronger electric and magnetic multipoles and is not considered in classical electrodynamics textbooks. The evolution of metamaterials, artificial materials with engineered macroscopic electromagnetic properties, has provided the tool for the realization of materials with a strong toroidal response and the experimental verification of its contribution to the multipole expansion. In this chapter, the analysis for the multipole expansion, with the toroidal multipoles included, is presented and their indispensable role is showcased in metamaterials consisting of dielectric metamolecules.

Optical vortices that have no radial symmetry and carry a fractional orbital angular momentum (OAM) have been studied intensively in the past several years. This interest is due to the fact that optical vortices with fractional OAM have found applications in quantum computing for generating entanglement of the OAM states of photon pairs. In this chapter, several laser beams with a fractional OAM are considered, including a three-parameter family of diffraction-free asymmetric elegant Bessel modes, a three-parameter family of asymmetric Bessel–Gauss beams, and a non-paraxial family of non-diffracting laser beams whose complex amplitude is proportional to the n-th order Lommel function of two variables. These beams are referred to as Lommel modes. Vortex Hermite–Gaussian modes are also considered; the latter are described by a complex amplitude proportional to the n-th order Hermite polynomial whose argument is a function of a real parameter. In addition, a new family of asymmetric Laguerre–Gaussian (aLG) laser beams is described. The beams have been derived via a complex-valued shift of the conventional LG beams in the Cartesian plane.

The structure of the focal region of a high-numerical aperture (NA) focusing system is determined by both the polarization and the complex amplitude distributions over the pupil plane. State-of-the-art optical tools provide a variety of capabilities for shaping light beams with the desired polarization and amplitude-phase properties. It should be noted that, although intended for similar purposes, these tools may vary substantially in the implementation complexity and cost. In this chapter, some relatively simple and convenient to implement phase diffractive structures to control the vector structure of the field in the focal region are discussed.

Besides scalar phase singularities (vortex phase, phase jumps), various special polarization states of vector fields exist. The most interesting of these is the cylindrical polarization state (radial or azimuthal). The mutual interrelation between optical phase vortices and polarization states, and the resulting angular momentum compensation or enhancement become especially important in a sharp or tight focus. Currently, cylindrical beams with radial or azimuthal polarization are being used successfully for the optical manipulation of micro- and nanoparticles as well as in microscopy, lithography, nonlinear optics, materials processing, and telecommunication applications. Here we demonstrate the conversion of cylindrically polarized laser beams from a radial to an azimuthal polarization, or vice versa, by introducing a higher order vortex phase singularity.

The following sections are included:

• Introduction to the Index
• Index