Quick start: Optical filter overview

In this quick start we use OghmaNano’s optical filter solver to calculate how light is reflected and transmitted by multilayer thin-film stacks at normal incidence. Such stacks can be designed as antireflection coatings, mirrors, or band-pass filters.

Background:

Light travelling through a thin film can be thought of as a forward and a backward wave. As the wave passes through a layer of thickness \(d\) and refractive index \(n\), it acquires a phase shift \(\delta = \tfrac{2\pi}{\lambda}\,n d\), where \(\lambda\) is the wavelength in free space. The behaviour of the wave in the layer can be written using a 2×2 transfer matrix \[ M = \begin{bmatrix} \cos(\delta) & \tfrac{i}{n}\sin(\delta) \\ i n \sin(\delta) & \cos(\delta) \end{bmatrix}, \] which relates the electric field amplitudes entering and leaving the layer.

For a stack of layers, the overall response is found simply by multiplying the matrices of all layers: \[ M_\text{total} = \prod_{j=1}^{N} M_j. \] Once the total matrix is known, the reflection and transmission of the stack can be calculated. If the incident medium has refractive index \(n_0\) and the substrate has refractive index \(n_s\), the reflection and transmission coefficients are extracted from \(M_\text{total}\), and the measurable reflectance and transmittance are given by \[ R = |r|^2, \qquad T = \frac{n_s}{n_0}\,|t|^2. \]

By adjusting the thicknesses and refractive indices of the layers, one can design filters with tailored optical properties. A single quarter-wave layer can suppress reflection at its design wavelength, while alternating high- and low-index quarter-wave layers produce a Bragg reflector with a strong stop band.

Getting started:

To start your first mode solver calculation, open the New simulations window from the File ribbon in the main window. Double-click on Mode Solver, and then double-click on 1D Slab Waveguide (TE), or transverse electric. Finally, save the new simulation to a folder on your disk.

1. Getting started: 1D slab (TE)

Once you have saved the simulation, the window in Figure 3 will appear. This shows a layer structure in the Epitaxy editor. The example consists of three layers: Layer 0, Layer 1, and Layer 2. The refractive index in Layer 1 is higher than in Layer 0 and Layer 2, forming a typical slab waveguide structure. Clicking the Play button starts the mode solver. The solver searches for modes supported within the structure. Because the solutions to the equations only exist at certain discrete wavelengths, not every wavelength will be supported. The Play button tells the solver to look for these supported modes.

The time taken depends on the wavelength range you choose and the complexity of your structure, so the search can take a little while. Once the search is complete, an outputs directory is created containing a snapshots folder (see Figure 4). By double-clicking on this folder, you can view the modes that the solver has found.

In Figures 5, 6, and 7 you can see three modes that the solver has found. To view these results, open the snapshots folder, then click the plus button and add E.csv to the list of fields to display. Using the sliders, you can move through the different modes that were calculated. The solver will show you which modes exist in the structure and what their field profiles look like.

Here, we show the first three harmonic modes that were found in the slab waveguide structure. These modes illustrate how light can be confined and guided in the device, depending on wavelength and geometry.

2. Switching to TM

In Optical → Mode calculator, change polarization to Transverse magnetic (TM), re-run, and reopen Snapshots. Due to boundary conditions at dielectric interfaces, TM modes show a characteristic field discontinuity at material boundaries (from continuity of D_⊥ rather than E_⊥). You should see slightly sharper jumps at core/cladding interfaces compared to TE.

6. Next steps

• Vary core thickness and index contrast to see cut-off behavior of higher-order modes.
• Increase wavelength sampling for smoother dispersion plots.
• Switch to TM in 2D and compare confinement vs. TE.
• Try the “more complex 2D waveguides” templates (rib/strip) for realistic photonics layouts.