We study nonlinear wave phenomena in hyperbolic and plasma-like dielectric isotropic metamaterials, dielectric-graphene (DG), dielectric-semiconductor (DS) and dielectric-metal (DM) plasma-like media (PM) (DGPM, DSPM, DMPM, respectively). When a THz beam passes through a layered DGPM in the presence of external magnetic field, we show the ability to effectively control the resonant complex nonlinear conductivity of graphene and modulation of the beam amplitude. In the hyperbolic nonlinear active IR field concentrator, the possibilities of (i) forming three types of focused nonlinear wave structures and (ii) the quasi-chaotic behaviour of the field amplitude inside the region of focusing in the above-threshold regime are demonstrated. Non-stationary regime for incident beam is included into consideration. When pulses in the IR range impinge a layer of a planar hyperbolic metamaterial with gain-active inclusions providing resonant nonlinear dissipation, the formed wave beam demonstrates pronounced synergistic behaviour with both “absorption” and “survival” phenomena. In a multilayer DMPM operating in the THz range, the transmission of a wave beam happens with the nonlinear medium transparency, whereas the medium nonlinearity is manifested via the nonlinear conductivity/nonlinear losses. In this case, quantum effects in thin metal layers were taken into account. They led, in particular, to nonlocality of the medium response. These and other theoretically revealed effects are experimentally realizable, provided with estimates for the parameters of structures and materials, and can be useful in creating effectively controllable nonlinear modulators, limiters, concentrators, sensors, devices with harmonic generation and frequency mixing, and other devices.
The investigation of hyperbolic metamaterials, shows that metal layers that are part of graphene structures, and also types I and II layered systems, are readily controlled. Since graphene is a nicely conducting sheet it can be easily managed. The literature only reveals a, limited, systematic, approach to the onset of nonlinearity, especially for the methodology based around the famous nonlinear Schrödinger equation [NLSE]. This presentation reveals nonlinear outcomes involving solitons sustained by the popular, and more straightforward to fabricate, type II hyperbolic metamaterials. The NLSE for type II metatamaterials is developed and nonlinear, non-stationary diffraction and dispersion in such important, and active, planar hyperbolic metamaterials is developed. For rogue waves in metamaterials only a few recent numerical studies exist. The basic model assumes a uniform background to which is added a time-evolving perturbation in order to witness the growth of nonlinear waves out of nowhere. This is discussed here using a new NLSE appropriate to hyperbolic metamaterials that would normally produce temporal solitons. The main conclusion is that new pathways for rogue waves can emerge in the form of Peregrine solitons (and near-Peregrines) within a nonlinear hyperbolic metamaterial, based upon double negative guidelines, and where, potentially, magnetooptic control could be practically exerted.
Metamaterial research is an extremely important global activity that promises to change our lives in many different
ways. These include making objects invisible and the dramatic impact of metamaterials upon the energy and medical
sectors of society. Behind all of the applications, however, lies the business of creating metamaterials that are not
going to be crippled by the kind of loss that is naturally heralded by use of resonant responses in their construction.
Under the general heading of active and tunable metamaterials, an elegant route to the inclusion of nonlinearity and
waveguide complexity coupled to soliton behavior suggested by forms of transformation dynamics is presented. In
addition, various discussions will be framed within a magnetooptical environment that deploys externally applied
magnetic field orientations. Light can then be directed to achieve energy control and be deployed for a variety of
outcomes. Quite apart from the fact that the manufacture of metamaterials is attracting such a lot of global attention,
the ability to control light, for example, in these materials is also immensely interesting and will lead to a new dawn
of integrated circuits and computers. Recognizing the role of nonlinearity raises the possibility that dramatic
manufacturing and applications are on the horizon.
Controlling losses in metamaterials has now reached an advanced stage, so that building up a range of
integrated waveguide devices based upon them is not only attractive from a fundamental point of view, but it
is going to be possible to imagine a number of special down-stream applications. The degree of control
obtained by manipulating planar metamaterial waveguides and interfaces is important and is popularly based
upon solitons of various kinds. Complete control is assured by invoking transformation optics, as will be
briefly demonstrated here.
Guided waves in metamaterials are attracting attention, even though, experimentally, there remain some
substantial questions about the fabrication of wave guides. Nonlinear guided optical waves have always been
attractive for their device potential, so the development of nonlinear waves in metamaterials is an important
direction to take and this is the basis of the discussion put forward by this paper. Given an effective medium
starting point, it is possible to highlight the metamaterial influences upon both exact nonlinear waves and the
soliton behaviour that is characteristic of the weakly nonlinear regime. This paper progresses through a
number of priorities that have been discussed in the literature. The outcomes are rapidly reviewed from the
point of view of putting the field into the context of both strongly nonlinear waves and spatial solitons, since
both scenarios emphasise the role of metamaterial control. Finally, the possibility of using magneto-optics as
an external control to modify the metamaterial influences is briefly displayed.
The history of optical solitons is fascinating and any theory of these has a weakly guiding foundation. Vortex generation
and propagation properties have also a beautiful history, and the possibility of generating them together with
magnetooptic control in plasmonic metamaterials will be discussed in detail. An emphasis will be placed on the fact that
spatial solitons have a lot of application possibilities, especially when placed into the context of materials being used in a
light-controlling light environment that is suitable for optical chips of the future. In addition, temporal solitons will also
be invoked. An initial emphasis will be placed upon narrow beams and extremely short pulses, but it will be pointed out
very strongly that detailed control of light-packets can also be introduced by using plasmonic metamaterials in the optical
frequency range. This feature requires an exact study of wave propagation in waveguides that are possibly tapered, or
simply just power controlled. To any designs that are proposed can be added the advantage of using magnetooptics. The
complicated structures that will be examined will include soliton-like channels near interfaces. Optically linear and
nonlinear metamaterials will be discussed in this context. The applications of the outcomes should lead to a new range of
optical switching.
A fascinating review of nonlinear waves in metamaterials is presented. The usual weakly nonlinear approximation is
dispensed with, and there is an emphasis upon complex waveguides. Many opportunities exist for elegant control using
the deployment of magnetooptic environments.
The creation of electromagnetic metamaterials is an important activity. The latter should anticipate the kind of
applications in which unique metamaterial behaviour can appear. This paper addresses nonlinear wave phenomena in
both the strongly and the weakly nonlinear regimes. It inevitably involves novel nonlinear guided waves and solitonic
beam activities. In this context, some magnetooptic control is introduced. In addition, the kind of structural complexity
that can lead to trapped rainbows will be briefly examined. Finally, some aspects are made of vortex control in a
diffraction-managed metamaterial is presented.
The creation of electromagnetic metamaterials that will operate at THz frequencies, and into the visible frequency range, is an extremely important task that points to far-reaching medical, data storage, and processing applications. It is imperative, therefore, that these properties be associated with complex systems that can sustain both guided and surface waves in the nonlinear regime, and to offer the possibility of tunability through the addition of a gyromagnetic environment. In particular, a magneto-optic part of a metamaterial guiding structure will exert a dramatic influence because it can readily take advantage of the types of nanostructured geometries that are coming into existence. If the nonlinearity is strong, the shape of the modal fields of nonlinear guided waves changes significantly with power, as demonstrated a long time ago. The investigation of spatial and temporal solitons in double negative metamaterials is important to the future of integrated optical structures which rely upon specialized data manipulation. Some examples of strongly nonlinear waves will be given and the magnetooptic influences will be reserved for soliton management.
A fundamental approach to a slowly varying amplitude formulation for nonlinear waves in metamaterials will be
established. The weakly nonlinear slowly varying amplitude approach will be critically examined and some
misunderstandings in the literature will be fully addressed. The extent to which negative phase behaviour has a
fundamental influence upon soliton behaviour will be exposed. The method will deploy nonlinear diffraction and a
special kind of diffraction-management. This is additional to a detailed modulation instability analysis. The examples
given involve waveguide coupling and a nonlinear interferometer. In addition, a strongly nonlinear approach will be
taken that seeks exact solutions to the nonlinear equations for a metamaterial. A boundary field amplitude approach will
be developed that leads to useful eigenvalue equations that expose, in a very clear manner, the possibility that new kinds
of waves can be generated.
There is now a global interest in the creation of creation of electromagnetic metamaterials. The substantive early work is
focused upon the GHz frequency range but almost immediately the desire to progress rapidly to the optical frequency
range gathered momentum. This is a natural desire because many applications operate at optical frequencies but the THz
range is also important for a range of medical applications as well. The concepts that underpin the need for
metamaterials, and their special properties, are explained in this article and why the creation of exotic, artificial,
molecules is required to produce material behaviour beyond any performance that could naturally be expected. It will be
shown that the major key lies in adding magnetic properties to special dielectric behaviour. This leads to composites that
have almost magical behaviour. This presentation will explore the current global experimental progress towards three-dimensional
metamaterials and will explain, in a straightforward manner, the concept of negative refraction that is
attracting such a lot of attention. The initial ideas, and even some of the early misconceptions, will be addressed and
clearly illustrated in a manner that enhances any understanding of the conceptual structure will be expressed. It will be
shown that even though negative refraction can be associated with both backward and forward waves, the novel
metamaterial concept is to associate backward wave phenomena with isotropic media, artificially endowed with negative
permittivity and permeability. The principle application shown here is to a nonlinear ring interferometer that is capable
of sustaining arbitrarily thin solitons or "optical needles" that can also be managed by an external magnetic field.
The question of whether stable, active metamaterials can be created is addressed, both through a discussion of absolute
instability and an analysis of a transmission-line that produces dispersion analogous to that of the familiar split-ring
resonator/wire-based metamaterial. Gain is introduced using negative conductance diodes, and it is shown that the
frequency bandwidth controls the window of stable gain. The diodes are located as lumped elements in the unit cell. It is
demonstrated that the production of a stable, active, negative phase frequency window is possible.
The fundamental approach to a slowly varying amplitude formulation for nonlinear waves in metamaterials will be
established. The weakly nonlinear slowly varying amplitude approach will be critically examined and some
misunderstandings in the literature will be fully addressed. The extent to which negative phase behaviour has a
fundamental influence upon soliton behaviour will be addressed and will include non-paraxiality, self-steepening and
nonlinear diffraction. A Lagrangian approach will be presented as a way of developing a clear picture of dynamical
behaviour. Exciting examples, involving waveguide and polarization coupling and interferometer systems will illustrate
the extent to which non-paraxiality, self-steepening and nonlinear diffraction will be required as part of the soliton
behaviour patterns, including coupler systems. In addition, a strongly nonlinear approach will be taken that seeks exact
solutions to the nonlinear equations for a metamaterial. The investigations will embrace "optical needles", or
autosolitons. A boundary field amplitude approach will be developed that leads to useful and elegant eigenvalue
equations that expose in a very clear manner the dependence of wave number upon the optical power density. All the
work will be beautifully illustrated with dramatic color-coded outcomes that will also embrace the soliton lens.
A discussion of gain control up to the THz frequency range is presented together with a study of diffraction-managed
solitons in metamaterials. Full dynamical simulations are used at every stage to illustrate the principles being evolved.
An interesting approach based upon the mapping of the complex frequency-plane onto the complex wave number-plane
is given as a way of demonstrating whether the offset of loss by using gain leads to a stable material. Nonlinear
behaviour is addressed through the possibility of soliton formation under the conditions for which nonlinear diffraction
can play a role whenever an attempt to manage the diffraction is made with a suitable combination of left-handed and
right-handed materials. All of this activity requires the modeling of curious artificial molecules but the computational
outcomes inspire confidence that is exemplified with exciting illustrations. The remit of control, exercised through
external influences such as an applied magnetic field, and cavity formation is briefly explored.
Negative phase velocity materials are engineered media that are currently enjoying a surge of interest due to their
interesting properties and potential applications, through negative refraction, to achieve cloaking that makes things
invisible. The literature is alive with papers devoted to the design of suitable metamaterials and there is a particular
desire to operate at THz frequencies and above. A full theory of gain control up to the THz frequency range is presented
together with a comprehensive study of diffraction-managed solitons. There are aspects of control that can be achieved
through externally imposed influences such as gyroelectromagnetic effects. Nonlinear behaviour is also intrinsic to the
Holy Grail quest for complete control, coupled to the possibility of beneficial competition between damping and gain.
The literature is alive with papers devoted to the design of metamaterials and there appears to be a particular desire to create photonic applications that will operate at THz frequencies and above. At one level the modelling of suitable artificial molecules is straightforward but nevertheless the approximations involved need to be able to inspire confidence for optical frequency operation. This presentation will set out a modelling activity that is known to be satisfactory only over certain frequency ranges. Split-ring and omega particles will be specifically investigated and the possibilities discovered will be related to the current experimental expertise. The detailed manner in which the constitutive relations can be controlled and the novel way in which an envelope equation emerges for even the most complex structure is exposed. The transmission and reflection properties of nano-structured materials will be discussed within a magneto-optic environment. Simulations of sub-wavelength transmission through holes in metallic and magneto-optic screens will be discussed using finite-difference time-domain (FDTD) methods. Modelling the interaction of light beams with metamaterials is developed, again using FDTD techniques, and it is shown that special care needs to be taken with structures that have sharp external edges. Finally, a summary of the problems surrounding efficient computations will be shown and some discussion of the role of genetic algorithms in metamaterial design will be featured.
Negative phase velocity metamaterials (NPM) are engineered media currently enjoying a surge of interest due to their interesting properties and potential applications. Their nonlinear behaviour will be intrinsic to the Holy Grail quest for power control. This is a hot topic that is only just being explored as evidenced by a rapidly increasing number of publications over the past few years. With the introduction of power comes the possibility of solitons and it is important to recognise that damping, arising from both the environment and the material, must be offset by the introduction of gain. In this context the investigation considers what are known as dissipative solitons, within a pumping, multi-stable configuration, designed as a ring or Fabry-Perot cavity. Several exciting scenarios will be presented and particular attention is devoted to the nonlinearity displayed by well-known 'artificial' molecules such as split rings and omega particles. The desire to create metamaterials that reach out to optical frequencies is acknowledged through a discussion of scalability. Detailed studies of the cavity stability regimes lead to some novel possibilities for cavity control. The presentation will be rounded off with a generalised theory of metamaterial behaviour in nonlinear environments that is based upon a novel approach using what is sometimes called the nonlinear Lorentz lemma. Extensive new numerical results will be used to illustrate the concepts outlined above.
A description of the fascinating coupling between gyrotropic media and negative refracting media will be presented. The article will address negative phase velocity media and particular types of dielectric-gyrotropic film-dielectric systems in which the applied magnetic field may result in a magneto-optic, or gyromagnetic, influence. The control features use a diverse family of dispersion
curves.
Access to the requested content is limited to institutions that have purchased or subscribe to SPIE eBooks.
You are receiving this notice because your organization may not have SPIE eBooks access.*
*Shibboleth/Open Athens users─please
sign in
to access your institution's subscriptions.
To obtain this item, you may purchase the complete book in print or electronic format on
SPIE.org.
INSTITUTIONAL Select your institution to access the SPIE Digital Library.
PERSONAL Sign in with your SPIE account to access your personal subscriptions or to use specific features such as save to my library, sign up for alerts, save searches, etc.