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<title>TE/TM plane wave propagation thorugh multilayered structures: a quick guide</title>
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<h1 align="center">TE/TM plane wave propagation through multilayered structures: a brief guide</h1>
<div class="content" align="justify">
<introduction>
<p>This guide provides a brief reference to the Graphical User Interface (GUI) that implements the propagation of a TE (Transverse
Electric)/TM (Transverse Magnetic) plane wave through a multilayered structure of media with different electromagnetic characteristics.
The incident wave is a TE/TM plane wave in the the <i>zy</i> plane (sinusoidal regime with temporal convention
<span class="inline_eqn"><i>e<sup>jωt</sup></span></i> ), traveling
from +<i>z</i> to -<i>z</i>.<br>
The GUI has four main output windows displaying the <i>x</i> component of the field, specifically the electric field or the magnetic
field when a TE or a TM wave is considered, respectively. The top left-hand figure shows the total field, superposition of
the progressive and of the regressive waves, which, on turn, are depicted in the top right-hand and in the bottom left-hand
figures. Finally, the bottom right-hand figure shows the field values corresponding to a vertical cut of the plane, specifically
for <i>y</i> = 0 m.
</p>
</introduction>
<h2>Contents</h2>
<div>
<ul>
<li><a href="#19">Installing the GUI</a></li>
<li><a href="#1">Running the GUI</a></li>
<li><a href="#11">GUI input parameters and buttons</a></li>
<ul>
<li><a href="#2">Frequency</a></li>
<li><a href="#3">Electric permittivity</a></li>
<li><a href="#4">Conductivity</a></li>
<li><a href="#5">Magnetic permeability</a></li>
<li><a href="#6">Z-coordinate of the interfaces</a></li>
<li><a href="#7">Incident field</a></li>
<li><a href="#8">Angle of incidence</a></li>
<li><a href="#9">Axes range</a></li>
<li><a href="#10">Number of samples of each axis</a></li>
<li><a href="#12">TE/TM wave selection</a></li>
<li><a href="#13">Real/Absolute values</a></li>
<li><a href="#14">Animate fields</a></li>
<li><a href="#15">Calculation details</a></li>
<li><a href="#16">Calculate</a></li>
<li><a href="#17">Stop animation</a></li>
<li><a href="#18">Help</a></li>
</ul>
</ul>
</div>
<br>
<h3>Installing the GUI<a name="19"></a></h3>
<p>To install the GUI, copy the files "PlaneWaveGUI.m" and "Help.html" to the same folder.</p>
<br>
<h3>Running the GUI<a name="1"></a></h3>
<p>To launch the GUI, open Matlab®, change the "Current Directory" to the folder where files have been copied. Afterwards, to start the GUI,
type "PlaneWaveGUI" at Matlab® prompt.</p>
<br>
<h3>GUI input parameters and buttons<a name="11"></a></h3>
<p>A brief description of the GUI elements (fields, buttons, options, etc.) is provided here:</p>
<h2>Frequency<a name="2"></a></h2>
<p>This field allows to specify the frequency of the plane wave, expressed in Hz. Obviously, only positive values are accepted.</p>
<h2>Electric permittivity<a name="3"></a></h2>
<p>This field allows to specify the values of the relative electric permittivity associated to the materials defined. Each entry
of the vector refers to a medium, starting from the one defined in the semispace <i>z</i> > 0 m. In fact, at least two materials should
be defined, whose interface is set in <i>z</i> = 0 m. Complex values of the electric permittivity (indicating power losses associated
to the material) are allowed (the imaginary part has to be negative, according to the temporal convention
<span class="inline_eqn"><i>e<sup>jωt</sup></span></i> ).
Both positive (dielectric) and negative (plasmas/double negative materials) values are accepted.
</p>
<h2>Conductivity<a name="4"></a></h2>
<p>This field allows to specify the values of the electric conductivity associated to the materials defined (imperfect dielectric
or good conductor). Each entry of the vector refers to a medium, starting from the one defined in the semispace <i>z</i> > 0 m. In
fact, at least two materials should be defined, whose interface is set in <i>z</i> = 0 m. Only real positive values are accepted.
</p>
<h2>Magnetic permeability<a name="5"></a></h2>
<p>This field allows to specify the values of the relative magnetic permeability associated to the materials defined. Each entry
of the vector refers to a medium, starting from the one defined in the semispace <i>z</i> > 0 m. In fact, at least two materials should
be defined, whose interface is set in <i>z</i> = 0 m. Complex values of the magnetic permeability (indicating power losses associated
to the material) are allowed (the imaginary part has to be negative, according to the temporal convention
<span class="inline_eqn"><i>e<sup>jωt</sup></span></i> ).
Finally, both positive (magnetic media) and negative (ferrites/double negative materials) values are accepted.
</p>
<h2>Z-coordinate of the interfaces<a name="6"></a></h2>
<p>This field allows to specify the <i>z</i> position (in meters) of the discontinuities between the defined materials. At least one
discontinuity in <i>z</i> = 0 m should be defined. As the plane wave travels from +<i>z</i> to -<i>z</i>, the position of the interfaces has to be
incrementally negative.
</p>
<h2>Incident field<a name="7"></a></h2>
<p>This field allows to specify the oscillation amplitude of the incident field. The value must be expressed V/m or
in A/m if a TE or a TM wave is considered, respectively. Only positive values are accepted.
</p>
<h2>Angle of incidence<a name="8"></a></h2>
<p>This field allows to specify the angle of incidence of the plane wave impinging on the first discontinuity. The angle is defined
by the normal to the wave fronts and the <i>y</i> axis and it increases in the counter clockwise direction starting from the <i>y</i> axis.
Therefore, 0° means normal incidence, 90° a wave traveling from -<i>y</i> to +<i>y</i> and -90° a wave traveling from +<i>y</i> to -<i>y</i>. The angle
must be expressed in degrees and only values comprised between -90° and 90° are accepted.
</p>
<h2>Axes range<a name="9"></a></h2>
<p>This field allows to specify the ranges of the <i>z</i> and <i>y</i> axes (in meters), thus causing both axes to have the same dimensions.
As the GUI defines at least two materials whose discontinuity is set in <i>z</i> = 0 m, such value must be included in the axes ranges.
</p>
<h2>Number of samples of each axis<a name="10"></a></h2>
<p>This field allows to specify the spatial discretization of the plane by entering the number of samples of each axis. Obviously
only values greater than 0 are accepted.
</p>
<h2>TE/TM wave selection<a name="12"></a></h2>
<p>This pop-up menu allows to choose between a TE or a TM wave. Results show the <i>x</i> component of the electric field or of the
magnetic field if a TE or a TM wave is selected, respectively.
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