Chapter 1 - Active Optical Metamaterials

Nonlinear Mode Interactions in the Wake of a Medium Height Roughness Element

Negative refractive index, perfect lenses and checkerboards: Trapping and imaging effects in folded optical spaces

An experimental study of the conditions for negative energy refraction and negative phase refraction in lossy metamaterials is provided. In hypothetical non‐lossy metamaterials, the angles of phase and energy refraction are one and the same. Using measured S‐parameters of split ring resonator–wire metamaterial samples, it is shown that negative refractive index is not a requirement for negative energy refraction in lossy metamaterials. It was assumed that the sample is effectively homogeneous and isotropic in the direction of wave propagation. For transverse‐electric polarisation, negative energy refraction with a positive refractive index was demonstrated.

This work presents a comprehensive analysis of electromagnetic wave propagation inside a two-dimensional photonic crystal in a spectral region in which the crystal behaves as an effective medium to which a negative effective index of refraction can be associated. It is obtained that the main plane wave component of the Bloch mode that propagates inside the photonic crystal has its wave vector k' out of the first Brillouin zone and it is parallel to the Poynting vector ( S' ? k'> 0 ), so light propagation in these composites is different from that reported for left-handed materials despite the fact that negative refraction can take place at the interface between air and both kinds of composites. However, wave coupling at the interfaces is well explained using the reduced wave vector ( k' ) in the first Brillouin zone, which is opposed to the energy flow, and agrees well with previous works dealing with negative refraction in photonic crystals.

A strategy to greatly broaden negative refractive index (NRI) band, reduce loss and ease bi-anisotropy of NRI metamaterials (MMs) has been proposed at terahertz frequencies. Due to the symmetric structure of the MM, the transmission and refractive index are independent to polarizations of incident radiations, and a broadband NRI is obtainable for the range of the incident angle from 0° to 26°. In addition, THz MMs’ properties such as transmission, phase and negative refraction exhibit a real-time response by controlling the temperature. The results indicate that the maximum bands of the negative and double-negative refraction are 1.66 THz and 1.37 THz for the temperature of 40 °C and 63 °C, respectively. The figure of merit of the MMs exceeds 10 (that is, low loss) as the frequency increases from 2.44 THz to 2.56 THz in the working temperature range, and the maximum figure of merit is 83.77 at 2.01 THz where the refractive index is −2.81 for a given temperature of 40 °C. Furthermore, the negative refraction of the MMs at the low loss band is verified by the classical method of the wedge, and the symmetric slab waveguide based on the proposed MM has many unique properties.

Negative refraction in multilayered metal-dielectric metamaterials is usually based on negative refractive indices or hyperbolic-like isofrequency surfaces. In this study, we reveal that ellipse-like isofrequency surfaces can also lead to negative refraction. This phenomenon is theoretically demonstrated by analyzing the group velocities of refracted beams based on the exact transfer-matrix method and verified by numerical simulation based on the finite-element method. The corresponding physics mechanism is investigated through the energy flow of the ellipse-like modes in the metallic and dielectric layers. The results are also compared with the case of energy flow of hyperbolic-like modes. Moreover, negative double refraction is realized because negatively refracted beams can be enabled by ellipse-like and hyperbolic-like isofrequency surfaces simultaneously.

In this dissertation, they have undertaken the challenge to understand the unusual propagation properties of the photonic crystal (PC). The photonic crystal is a medium where the dielectric function is periodically modulated. These types of structures are characterized by bands and gaps. In other words, they are characterized by frequency regions where propagation is prohibited (gaps) and regions where propagation is allowed (bands). In this study they focus on two-dimensional photonic crystals, i.e., structures with periodic dielectric patterns on a plane and translational symmetry in the perpendicular direction. They start by studying a two-dimensional photonic crystal system for frequencies inside the band gap. The inclusion of a line defect introduces allowed states in the otherwise prohibited frequency spectrum. The dependence of the defect resonance state on different parameters such as size of the structure, profile of incoming source, etc., is investigated in detail. For this study, they used two popular computational methods in photonic crystal research, the Finite Difference Time Domain method (FDTD) and the Transfer Matrix Method (TMM). The results for the one-dimensional defect system are analyzed, and the two methods, FDTD and TMM, are compared. Then, they shift their attention only to periodic two-dimensional crystals, concentrate on their band properties, and study their unusual refractive behavior. Anomalous refractive phenomena in photonic crystals included cases where the beam refracts on the ''wrong'' side of the surface normal. The latter phenomenon, is known as negative refraction and was previously observed in materials where the wave vector, the electric field, and the magnetic field form a left-handed set of vectors. These materials are generally called left-handed materials (LHM) or negative index materials (NIM). They investigated the possibility that the photonic crystal behaves as a LHM, and how this behavior relates with the observed negatively refractive phenomena. They found that in the PC system, negative refraction is neither a prerequisite nor guarantees left-handed behavior. They examined carefully the condition to obtain left-handed behavior in the PC. They proposed a wedge type of experiment, in accordance with the experiment performed on the traditional LHM, to test these conditions. They found that for certain frequencies the PC shows left-handed behavior and acts in some respects like a homogeneous medium with a negative refractive index. they used the realistic PC system for this case to show how negative refraction occurs at the interface between a material with a positive and a material with a negative refractive index. Their findings indicate that the formation of the negatively refracted beam is not instantaneous and involves a transient time. With this time-dependent analysis, they were able to address previous controversial issues about negative refraction concerning causality and the speed of light limit. Finally, they attempt a systematic study of anomalous refractive phenomena that can occur at the air-PC interface. They observe cases where only a single refracted beam (in the positive or negative direction) is present, as well as cases with birefringence. they classify these different effects according to their origin and type of propagation (left-handed or not). For a complete study of the system, they also obtain expressions for the energy and group velocities, and show their equality. For cases with very low index contrast, band folding becomes an artificiality. They discuss the validity of their findings when they move to the limit of photonic crystals with a low index modulation.

Phase compensating effect in left-handed materials

The phenomenon of negative refraction has been demonstrated experimentally and by numerical simulation assuming Drude and Lorentz models for the permittivity and permeability. It has been assumed that a negative refractive index results in negative refraction and hence will lead to a variety of exciting applications for metamaterials. Loss cannot be avoided in real metamaterials and in this paper, we analyze the effect of loss on negative refraction using experimentally extracted data for the permittivity, permeability and refractive index of a combined wire-Split Ring Resonator sample and for a sample with alternately oriented split ring resonators. Both samples are very lossy in the plasmonic resonance region and both display a negative refractive index. We show that obliquely incident waves on such samples may not always lead to negative refraction due to the effect of losses in the material.

Recently there has been a great deal of interest in an unusual category of material, that is, a material that exhibits negative refractive index or more generally negative group velocity. Perhaps the most immediate application of this type of material is in an area known as total and negative refraction, which may potentially lead to many novel optical devices. The reason that the phenomenon of total and negative refraction has become so interesting to the physics community is also due largely to the notion that this phenomenon would never occur in conventional materials with positive refractive index. It turns out that total and negative refraction can be realized even in natural crystalline materials or in artificial materials (e.g. photonic crystals) without negative (effective) refractive index. In this brief review, after providing a brief historic account for the research related to finding materials with negative group velocity and achieving negative refraction, we discuss the three primary approaches that have yielded experimental demonstrations of negative refraction, in an effort to clarify the underlying physics involved with each approach. A brief discussion on the subwavelength resolution application of the negative (effective) refractive index material is also given.

Guiding optical energy in metal–dielectric nanostructures by the use of plasmon excitations known as surface plasmons has received much attention over the past few decades. The diverse applications of this technology span many areas in modern science, including scanning near-field optical microscopy (SNOM), bio-medical imaging and sensing, surface-enhanced Raman spectroscopy (SERS), and the realization of nanophotonic circuit elements. Plasmonic waveguides play a prominent role in the efficient operation of these devices, which are responsible for carrying optical signals in subwavelength dimensions. The guided optical modes suffer from propagation losses that arise due to various factors, such as scattering from surface imperfections in waveguides, absorption losses in dielectrics, and ohmic heating in metals. Even though scattering losses may be minimized by employing cutting-edge fabrication techniques that stem from the rapid advancements in material engineering, and dielectric losses are often negligibly small, the metal losses are high in magnitude and thus cannot be overlooked. Since metals are essential to sustain and guide the plasmonic modes, metal losses cannot be entirely eliminated. However, these losses may be compensated by doping the dielectric with rare-earth ions and providing optical gain via pumping. Since the amount of optical gain that can be supplied is practically limited, it is vital that waveguides are designed in such a way that the detrimental effects of metal losses are minimal. Waveguides of different geometrical shapes and arrangements have been identified as candidates for plasmonic waveguides, such as planar waveguides, circular cylinders, waveguides with square and triangular cross-sections, metal wedges and grooves, and linear chains of metal and metal–dielectric composite particles. These geometries have their own merits and demerits, in terms of the propagation losses and mode confinement. In this dissertation, the focus is on planar and circularly cylindrical geometries, and a number of both active and passive multi-layer structures are examined numerically, as well as analytically, for the efficient propagation of plasmonic modes. The effect of the geometrical parameters of the waveguide on propagation characteristics is investigated below the plasmon resonance frequency. Considering a planar waveguide consisting of a finite dielectric layer on a thick metal, it is shown that the guided mode experiences maximal modal gain at a particular thickness of the optically pumped dielectric layer. The threshold gain required to fully compensate for the losses (critical gain) in a metal–dielectric– metal (MDM) waveguide of infinite extent is estimated analytically, and an exact analytical expression for the confinement factor is derived. The more realistic case of an MDM structure with finite metal layers is also investigated, and it is revealed that thicknesses of metal/dielectric layers can be adjusted to ensure the furthest propagation of the guided mode. When the dielectric region is pumped to provide optical gain, the losses may be suppressed by minimal pump power at a particular choice of geometrical parameters. Additionally, it is shown that the gain experienced by the mode also becomes minimal, depending on the waveguide geometry. An exact analytical expression for the confinement factor is also presented. For a dielectric–metal–dielectric waveguide capped with metal, an approximate analytical solution for the dispersion equation is derived. The optimal geometrical parameters that yield the furthest propagation of the mode and compensation of losses with minimal optical gain are estimated analytically. Furthermore, approximate analytical expressions for the critical gain and the confinement factor are derived. Several composite cylindrical nanowire structures are also investigated for plasmonic guiding. For a nanowire consisting of a dielectric core and a metal cladding, it is shown that the critical gain becomes minimal at a particular cladding thickness. Similarly, the geometrical parameters of metal-core dielectricclad nanowires can also be chosen to lower the material gain requirement. Cylindrical MDM nanowires are also investigated, and it is shown that the guided mode can be strongly confined within the dielectric layer. The existence of optimal nanowire geometry that enables maximum propagation length of the mode and compensation of metal losses with minimal material gain is found.

Active nanoplasmonic metamaterials, pumped above lasing threshold, can exhibit dynamic competition between bright, radiative and dark, trapped modes of the structure. We study the spatio-temporal mode competition and explore methods of mode control.

Metamaterials are artificially engineered structures that have properties, such as a negative refractive index, not attainable with naturally occurring materials. Negative-index metamaterials (NIMs) were first demonstrated for microwave frequencies, but it has been challenging to design NIMs for optical frequencies and they have so far been limited to optically thin samples because of significant fabrication challenges and strong energy dissipation in metals. Such thin structures are analogous to a monolayer of atoms, making it difficult to assign bulk properties such as the index of refraction. Negative refraction of surface plasmons was recently demonstrated but was confined to a two-dimensional waveguide. Three-dimensional (3D) optical metamaterials have come into focus recently, including the realization of negative refraction by using layered semiconductor metamaterials and a 3D magnetic metamaterial in the infrared frequencies; however, neither of these had a negative index of refraction. Here we report a 3D optical metamaterial having negative refractive index with a very high figure of merit of 3.5 (that is, low loss). This metamaterial is made of cascaded 'fishnet' structures, with a negative index existing over a broad spectral range. Moreover, it can readily be probed from free space, making it functional for optical devices. We construct a prism made of this optical NIM to demonstrate negative refractive index at optical frequencies, resulting unambiguously from the negative phase evolution of the wave propagating inside the metamaterial. Bulk optical metamaterials open up prospects for studies of 3D optical effects and applications associated with NIMs and zero-index materials such as reversed Doppler effect, superlenses, optical tunnelling devices, compact resonators and highly directional sources.

Recently, a negative refractive index (NRI) lens using composite right/left handed transmission line (CRLH-TL) has been studied [1]. Negative refraction phenomenon has been investigated by a flat [2], and a concave lens [3]. And the CRLH-TL composed of the cut-off parallel plate waveguide and dielectric resonators was proposed as low-loss structure [4]. Authors has been investigated the potential of the shaped NRI lens for wide angle beam scanning [5]. And effects of the improvement of wide angle scanning characteristics and the miniaturization of the lens antenna using the NRI material were clarified. In this paper, a metamaterial lens antenna using dielectric resonators for wide angle beam scanning is presented. The lens antenna is composed of the radiator, the parallel plate waveguide and the NRI lens. Radiation characteristics and the loss of the NRI lens are discussed.

This work proposes a double quantum dot (DQD) system, with a wetting layer (WL) is included, to study the negative refractive index (NRI) under the application of the electric fields: pump, probe, and fields between WL-QD state, in addition to the magnetic field. The density matrix theory is used to write the equation of motion and an orthogonalized plane wave is used between WL-QD states. The results show that the DQD system exhibit NRI ordinarily until with pump and probe signals, only, due to the manipulation between states. A high NRI corresponding to neglected absorption is obtained under applied electric fields between QD-QD, the conduction (CB) and valence bands (VB) WL-QD fields. It is shown that the main requirement in increasing NRI is the high electric gain connected with a low magnetic one. This can be obtained under five applied electric fields in addition to a high VB WL-QD electric field. Neglecting WL reduces NRI by ~ 16 times. In single QD, the NRI is very small compared with DQD.