# Drude-Lorentz MIM Waveguide (MIMwaveguideT.pre)

## Problem Description

A metal-insulator-metal (MIM) waveguide can propagate optical frequency electromagnetic radiation due to the effective negative index material property of the metal at those frequencies. This negative index material is represented with a time-domain Drude model dielectric, which can support a wide range of frequencies and wide bandwidth.

In addition to the MIM waveguide, a section of the insulator is removed, and replaced with a resonant absorber material, using a time-domain version of the traditional Lorentz material.

Fig. 277 Longitudinal electric field in the MIM waveguide.

Fig. 278 Transverse electric field in the MIM waveguide.

A spatial gaussian waveform is incident on the edge of the MIM waveguide, coupling to it, and propagating down the length of the waveguide until it encounters the Lorentz material inclusion, where the wave is absorbed. For the incident wave to couple effectively to the MIM waveguide, the spatial size of the gaussian waveform must be a good match to the size of the waveguide, or a large portion of the incident wave will scatter off the structure, rather than coupling to it.

Also, the width, strength, and natural frequency of the Lorentz material inclusion determines whether the wave is reflected, absorbed, or transmitted when it encounters the inclusion.

The length of the MIM waveguide, and the direction of wave propagation is in the x-direction. The width of the waveguide is in the z-direction, and the height of the waveguide is in the y-direction. The waveguide sits atop an insulator substrate, and is surrounded by air. The boundaries of the simulation are ports, allowing for incoming and outgoing waves.

This simulation is the primary example demonstrating the use of the general purpose Drude-Debye-Lorentz-Dielectric macro file, DrudeDebyeLorentzDielectric. Calls to these macros can be found by searching the input file for the string “DDLD”.

This simulation can be performed with a VSimEM license.

## Opening the Simulation

The MIM waveguide example is accessed from within VSimComposer by the following actions:

• In the resulting Examples window expand the VSim for Microwave Devices option.
• Expand the Cavities and Waveguides (text-based setup) option.
• Select “Drude-Lorentz MIM Waveguide (text-based setup)” and press the Choose button.
• In the resulting dialog, create a New Folder if desired, and press the Save button to create a copy of this example.

The basic variables of this problem will now be alterable via the text boxes in the left pane of the Setup Window, as shown in Fig. 279.

Fig. 279 Setup Window for the MIMwaveguideT example.

## Input File Features

The input file allows the user to choose the waveguide geometry parameters, the material properties of the Drude metal, insulator, and Lorentz inclusion, and the frequency and spatial size of the incident wave.

The input file also contains a parameter to adjust the spatial resolution of the mesh.

Default parameters are selected to correspond to violet light, a Drude material corresponding to silver, SiO2 insulator (and substrate), and a Lorentz material corresponding to AlAs. The default variable values can be compared to the well known material properties of these materials to establish the exact correspondence to the well-known mathematical descriptions of the Drude and Lorentz models.

## Running the simulation

After performing the above actions, continue as follows:

• Proceed to the Run Window by pressing the Run button in the left column of buttons.
• To run the file, click on the Run button in the upper left corner of the right pane. You will see the output of the run in the right pane. The run has completed when you see the output, “Engine completed successfully.” This is shown in Fig. 280.

Fig. 280 The Run Window at the end of execution.

## Visualizing the results

After performing the above actions, continue as follows:

• Proceed to the Visualize Window by pressing the Visualize button in the left column of buttons.

The results are best viewed by looking at the $$y$$ component of the electric field. To view the fields:

• Expand Scalar Data
• Expand edgeE
• Select edgeE_y
• Select the Clip All Plots checkbox
• Move the dump slider forward in time

You can add the structure by expanding Geometries and selecting the poly box. The field is shown in Fig. 281.

Fig. 281 Visualization of the $$E_y$$ field component.

We can see that fields are well coupled between the two metal layers of the waveguide, with only some small leakage, and transient behavior at the entrance. The fields then diminish abruptly at the inclusion, where the wave is mostly absorbed.