 # The Plane Wave Reflection Model-Dual Boundary

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Introduction

The lab, development of lab 1, is used the plane wave reflection model-dual boundary (PWRM-DR) instead of single mode in lab 1. That means the plane wave interacting between two shaded planes between three materials. This gave us the idea it react at the boundary by displaying the two points of views of planes waves which are 3D mode and plane mode like in lab 1. This lab is about behaviour of three materials managed by changing the relative permittivity or epsilon and conductivity or sigma and also the frequency and angle of the wave that hit the boundary can be altered. More tricky part is considering the ancient angle to get right propagated wave as the right incident angle range is quite narrow to capture. We will discuss about it later in procedure.

Investigation 1 is about how the plane waves react between two dielectric materials separated by thin metallic film and parallel plate that is the two metallic alongside apart by dielectric. First, to consider the thickness of metallic, we will use the skin depth calculated in lab1 and determine how the transmission and reflectance change according to different skin depths. Moreover, how the plane waves transmitted and reflected while the alternation of incident angle happens. After that, parallel plane waveguides are determined in investigation 1.2 and the incidence angle where the parallel plate waveguide propagates in y direction is investigated. Additionally, the effect of plane waves by increasing the thickness of layer 2, dielectric is conceived.

On the other hand, reflection at dielectric/dielectric boundaries is determined in investigation 2 where half wave resonator and anti-reflection coating is familiarized. If dielectric material is m λ/2 thick, then signals with wavelength λ pass through; is called half resonator. And anti-reflecting coating is when almost no reflection occurs. Lastly, the Slab Waveguide has been considered in investigation 2.3. We would expect plane waves to be propagated in y direction and total reflection happens.

Procedure

Investigation 1

Firstly, the materials' behaviours are manipulated on PWRM-DB, the perpendicular (TE) polarisation is set and frequency which is the last digit of one of us student number is chosen. In this task we need to set thickness of layer 2 to 5 skin depths which is calculated in lab 1 so the changes in transmission and reflectance magnitude are supposed to display. Normally, 5 skin depth is used not to be seen the field from the other side; is called rule of thumb. Continuously, the magnitude of reflectance and transmission, are recorded as incident angle increases. And the details are recorded into excel and the graph have been plotted for considering plane wave alternation according to incident angle. Similarly, it is said to do the same thing also with parallel (TM) polarisation. All the steps are repeated after changing TE to TM.

The next task in investigation1 is to consider where parallel plate waveguide mode propagates in y direction the second metallic interface can be placed to get a parallel plate waveguide. To be so the incident angle is affected so that the incident angle is adjusted till the reflectance angle become infinity. Furthermore, thte effect of thickness of layer 2 on plane waves has been discovered on PWRM-DB by doubling and troubling the layer thickness.

Investigation 2

To create a half wave resonator, the thickness of layer 2 is needed to be calculated using the following equations.

λ_2=λ_0/√(ε_2 )

And layer 2 is supposed to be m λ_2/2 thick.

Analyze the calculation with PWRM-DB. However, the half wave resonator only works at particular incident angle so the incident angle is adjusted and reflectance magnitude are recorded and plotted the graph to consider where the layer is no longer operating effectively.

The next step is to find the incident angle at anti reflection coating point. Before it, we have to calculate the second layer permittivity and thickness using the same equation in previous task and the thickness of layer 2 should be λ_2/4 in this case. And then, the same way goes to anti reflecting coat like half resonator to find the right incident angle.

Results

Thin Metallic Film

Layer 1 ε_r=1 σ=0 Polarisation=TE

Layer 2 ε_r=1 σ=1×〖10〗^5 s/m Frequency= 66GHz

Layer 3 ε_r=1 σ=0 Pulse Width=20

Incident from Layer 1

(a)

The thickness of layer 2 was set to 5 skin depths(i:e:5×3μm) and the Magnitude and the phase of the reflectance was measured for normal incident wave from layer 1 and obtained the following results.

Figure 1 - 3D view of the plane wave propagation though thin metallic film.

Figure 2 - Results obtained for 5 skin depth thicknesses

(b). The same procedure above in part (a) was carried out for 4,3,2,1 and 0.5 skin depths and the following results were obtained.

Reflectance Transmission

Layer 2 Thickness

in Skin depths Magnitude Phase Magnitude Phase

4 0.99196 179.511 0.00341014 -65.6889

3 0.992141 179.57 0.00533714 -39.3641

2 0.990564 179.689 0.00859177 -18.0952

1 0.982536 179.84 0.0173539 -4.63612

0.5 0.965829 179.919 0.0341566 -1.20018

Table 1 - Reflectance and Transmission Phase & Magnitude for different layer-2 thicknesses

Reflection: From the results we observe that when the thick ness of material 2 is decreased from 5 skin depths to 0.5 the field penetration of the metallic layer started increasing at 1 skin depth and below so considerable amount of field is penetrating into material 3.

(c)

Experimented the behaviour of the transmission magnitude with different incident angles(by increasing the incident angle from 0^0 to 〖90〗^0 in steps of 〖10〗^0)

Incident Angle Transmission Magnitude Reflectance Magnitude

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