11 research outputs found
Dyakonov-Tamm surface waves featuring Dyakonov-Tamm-Voigt surface waves
The propagation of Dyakonov-Tamm (DT) surface waves guided by the planar
interface of two nondissipative materials and was investigated
theoretically and numerically, via the corresponding canonical boundary-value
problem. Material is a homogeneous uniaxial dielectric material whose optic
axis lies at an angle relative to the interface plane. Material is
an isotropic dielectric material that is periodically nonhomogeneous in the
direction normal to the interface. The special case was considered in which the
propagation matrix for material is non-diagonalizable because the
corresponding surface wave-named the Dyakonov-Tamm-Voigt (DTV) surface wave-has
unusual localization characteristics. The decay of the DTV surface wave is
given by the product of a linear function and an exponential function of
distance from the interface in material ; in contrast, the fields of
conventional DT surface waves decay only exponentially with distance from the
interface. Numerical studies revealed that multiple DT surface waves can exist
for a fixed propagation direction in the interface plane, depending upon the
constitutive parameters of materials and . When regarded as functions of
the angle of propagation in the interface plane, the multiple DT surface-wave
solutions can be organized as continuous branches. A larger number of DT
solution branches exist when the degree of anisotropy of material is
greater. If then a solitary DTV solution exists for a unique
propagation direction on each DT branch solution. If , then no
DTV solutions exist. As the degree of nonhomogeneity of material decreases,
the number of DT solution branches decreases.Comment: arXiv admin note: text overlap with arXiv:1910.1097
Surface-plasmon-polariton wave propagation supported by anisotropic materials: multiple modes and mixed exponential and linear localization characteristics
The canonical boundary-value problem for surface-plasmon-polariton (SPP)
waves guided by the planar interface of a dielectric material and a plasmonic
material was solved for cases wherein either partnering material could be a
uniaxial material with optic axis lying in the interface plane.Numerical
studies revealed that two different SPP waves, with different phase speeds,
propagation lengths, and penetration depths, can propagate in a given direction
in the interface plane; in contrast, the planar interface of isotropic
partnering materials supports only one SPP wave for each propagation direction.
Also, for a unique propagation direction in each quadrant of the interface
plane, it was demonstrated that a new type of SPP wave--called a
surface-plasmon-polariton-Voigt (SPP-V) wave--can exist. The fields of these
SPP-V waves decay as the product of a linear and an exponential function of the
distance from the interface in the anisotropic partnering material; in
contrast, the fields of conventional SPP waves decay only exponentially with
distance from the interface. Explicit analytic solutions of the dispersion
relation for SPP-V waves exist and help establish constraints on the
constitutive-parameter regimes for the partnering materials that support
SPP-V-wave propagation
On Dyakonov-Voigt surface waves guided by the planar interface of dissipative materials
Surrogate modelling has become an important topic in the field of uncertainty quantification as it allows for the solution of otherwise computationally intractable problems. The basic idea in surrogate modelling consists in replacing an expensive-to-evaluate black-box function by a cheap proxy. Various surrogate modelling techniques have been developed in the past decade. They always assume accommodating properties of the underlying model such as regularity and smoothness. However such assumptions may not hold for some models in civil or mechanical engineering applications, e.g., due to the presence of snap-through instability patterns or bifurcations in the physical behavior of the system under interest. In such cases, building a single surrogate that accounts for all possible model scenarios leads to poor prediction capability. To overcome such a hurdle, this paper investigates an approach where the surrogate model is built in two stages. In the first stage, the different behaviors of the system are identified using either expert knowledge or unsupervised learning, i.e. clustering. Then a classifier of such behaviors is built, using support vector machines. In the second stage, a regression-based surrogate model is built for each of the identified classes of behaviors. For any new point, the prediction is therefore made in two stages: first predicting the class and then estimating the response using an appropriate recombination of the surrogate models. The approach is validated on two examples, showing its effectiveness with respect to using a single surrogate model in the entire space
On Dyakonov-Voigt surface waves guided by the planar interface of dissipative materials
Dyakonov-Voigt (DV) surface waves guided by the planar interface of (i)
material which is a uniaxial dielectric material specified by a relative
permittivity dyadic with eigenvalues and , and
(ii) material which is an isotropic dielectric material with relative
permittivity , were numerically investigated by solving the
corresponding canonical boundary-value problem. The two partnering materials
are generally dissipative, with the optic axis of material being inclined
at the angle relative to the interface plane.
No solutions of the dispersion equation for DV surface waves exist when
. Also, no solutions exist for ,
when both partnering materials are nondissipative. For , the degree of dissipation of material has a profound effect on
the phase speeds, propagation lengths, and penetration depths of the DV surface
waves. For mid-range values of , DV surface waves with negative phase
velocities were found. For fixed values of and in
the upper-half-complex plane, DV surface-wave propagation is only possible for
large values of when is very small