Photonic Crystal Tutorial: Simulate a Photonic Crystal and Waveguide

🎯 Learning objectives

Run your first photonic crystal FDTD simulation in OghmaNano.
Use optical snapshots and detectors to watch light propagate and measure it.
Compute and interpret a transmission spectrum (|E_out|²/|E_in|²).
See how the pillar radius shifts the photonic band, and build a photonic crystal waveguide.

⏱ Estimated time

Steps 1–3 (build and run): 5–10 min
Step 4 (snapshots): 5–10 min
Step 5 (detectors and transmission): 10–15 min
Step 6 (tuning the radius): 10–15 min
Step 7 (crystal editor and waveguide): 15–20 min
Total: around 1 hr depending on how much you explore.

Scanning electron microscope style image of a two-dimensional photonic crystal consisting of a periodic array of air holes etched into a dielectric slab, illustrating the type of structure commonly used to control and guide light — A scanning electron microscope (SEM) style view of a photonic crystal. The periodic array of holes creates a spatially varying refractive index which can be used to confine, guide, and manipulate light. Photonic crystals form the basis of many integrated photonic devices including waveguides, resonators, and optical filters.

1.Introduction to Photonic Crystals and Waveguides

A photonic crystal is an optical structure whose refractive index varies periodically on the scale of the wavelength of light. A common example is a dielectric slab patterned with a regular array of air holes, as shown in ??. This periodic structure creates a photonic band gap, a range of wavelengths that cannot propagate through the crystal. In many ways this is analogous to the electronic band gap found in semiconductors, except that it affects photons rather than electrons. By introducing a deliberate defect into the lattice, such as removing a row of holes, it becomes possible to create optical modes inside the band gap. Light can then be confined and guided through the defect region, even around sharp bends with very low loss. These photonic crystal waveguides form the basis of many integrated photonic devices including optical interconnects, resonators, filters, sensors, and wavelength-selective components.

In this tutorial you will use OghmaNano's finite-difference time-domain (FDTD) solver to build and simulate a two-dimensional photonic crystal. You will learn how to generate a periodic lattice using the step editor, launch light into the structure using FDTD light sources, visualise the electromagnetic field distribution, and calculate the transmission spectrum as a function of wavelength using FDTD detectors and spectral extraction. By changing the lattice geometry you will see how the photonic band gap shifts, and by introducing a defect you will create a photonic crystal waveguide and observe guided light propagation through the structure.

Photonic crystals are widely used in modern integrated photonics because they provide precise control over the flow of light while occupying only a small area on a chip. Understanding how photonic band gaps arise and how defects can be used to manipulate optical modes is therefore an important step towards designing advanced photonic devices.

2. Creating a New Photonic Crystal Simulation

Start OghmaNano from the Windows Start menu, then click New simulation to open the library of available device types, shown in ??.

In the New simulation window (??) double-click FDTD examples. This opens the list of optical/FDTD templates shown in ??, which includes a Fabry–Perot cavity, free space, an integrated photonics ring resonator, a Mach–Zehnder modulator and several waveguides. For this tutorial double-click Photonic crystal. When prompted, save the simulation to a folder you have write access to.

💡 Tip: For best performance save to a local drive such as C:\. Simulations stored on network, USB, or cloud folders (e.g. OneDrive) can run slowly due to heavy read/writes.

OghmaNano new simulation window listing device categories such as organic solar cells, OLEDs, OFETs, perovskites, ray tracing, and FDTD examples — The *New simulation* window provides a library of device types and example projects. Double-click an icon to open a preconfigured simulation. For photonic crystals, double-click the **FDTD examples** icon to reveal the optical templates.

OghmaNano FDTD examples list showing Fabry-Perot cavity, free space, integrated photonics ring resonator, photonic crystal, photonic-xtal trumpet, silicon Mach-Zehnder modulator, and tapered 975 nm waveguide — The *FDTD examples* folder lists ready-to-run optical structures. Each entry opens a preconfigured FDTD simulation that you can modify. Double-click **Photonic crystal** to load the structure used in this tutorial.

3. Run the simulation

Once saved, the main window opens (see ??). The device is an array of dielectric pillars (the red tubes) sitting between two thin detector planes: a purple input detector near the source and a green output detector on the far side. Use the xy/yz/xz buttons to orient the view. Click Run simulation (the blue play icon) or press F9. On slower machines the FDTD calculation may take a little while.

When the run finishes, open the Output tab (??) to browse the files the solver has written. Double-clicking any file opens it in the appropriate viewer.

Main OghmaNano interface showing the Run Simulation button and a 3D view of a photonic crystal made from a square array of red dielectric pillars, with purple and green detector planes. — The main *OghmaNano* interface after loading the photonic crystal. The 3D panel shows the array of dielectric pillars together with the input (purple) and output (green) detector planes. Press the **Run Simulation** button (or `F9`) to start the FDTD calculation.

OghmaNano Output tab while the FDTD simulation is running, showing progress messages, solver initialization and time-step information. — While the simulation is running the *Output* tab displays progress information from the FDTD solver, including device initialization, detector setup and the current simulation time step.

OghmaNano Output tab displaying the simulation working directory with result files such as detector0, detector1, snapshots, power.dat, and device.csv. — The *Output* tab exposes the working directory for the simulation. Key items are the `snapshots` folder (time snapshots of the field), and the `detector0` and `detector1` folders, which hold the spectra recorded by the input and output detectors. Double-clicking a file or folder opens it.

4. Watch the field propagate

Double-click the snapshots folder to open the snapshot viewer (??). The plotted file is Ey.csv — one component of the electric field — shown as a coloured wireframe surface, where colour and height both encode the field strength in V/m.

Drag the slider underneath the plot to step through time. You will see the launched pulse spread out from the source on the left, strike the photonic crystal, and partially scatter and transmit through it. Watching the field evolve is the most intuitive way to confirm the simulation is doing what you expect before you trust the numbers.

OghmaNano simulation snapshot viewer showing the Ey component of the electric field as a coloured wireframe surface, with a time slider beneath the plot. — The snapshot viewer plotting `Ey.csv` as a wireframe.

Early-time snapshot of the electric field interacting with the photonic crystal. — An early-time snapshot showing the pulse entering the photonic crystal.

Later-time snapshot showing the electric field after propagating through the photonic crystal. — A later snapshot showing the field after propagating through the crystal.

5. Detectors and the transmission spectrum

Now look at what the two detectors recorded. From the Output tab open the detector0 and detector1 folders; each contains a file called lam_E.csv, which is the wavelength-resolved field intensity |E|² arriving at that detector. The two detectors are the purple and green grids you can see in the device view.

Opening lam_E.csv in detector0 gives the input spectrum (??): this is the broadband pulse launched at the structure, with most of its energy around 900 nm. Opening lam_E.csv in detector1 gives the output spectrum (??), plotted on a logarithmic axis. Notice how heavily the light is attenuated at most wavelengths — the photonic crystal blocks them.

Comparing two raw spectra by eye is awkward, so the detector folder also contains lam_norm.csv, the ratio |E_Output|²/|E_Input|². This is the transmission spectrum of the photonic crystal. Double-click it to obtain ??.

The clear peak just above 1000 nm is the band of wavelengths the photonic crystal lets through; the strongly suppressed regions on either side are the photonic band gap, where propagation is forbidden. In other words, this single curve tells you both what the crystal transmits and where its band gap sits.

Input detector spectrum lam_E.csv showing |E| squared versus wavelength on a linear axis, with a broad peak near 900 nm. — The input detector (`detector0/lam_E.csv`): the broadband pulse incident on the crystal, peaking near 900 nm. This is the reference against which the output is compared.

Output detector spectrum lam_E.csv showing |E| squared versus wavelength on a logarithmic axis, strongly attenuated across most of the band. — The output detector (`detector1/lam_E.csv`) on a log scale. Most wavelengths are suppressed by several orders of magnitude because they fall inside the photonic band gap.

Transmission spectrum, the ratio of output to input field intensity, showing a single sharp peak just above 1000 nm. — The transmission spectrum |E_Output|²/|E_Input|² from `lam_norm.csv`. The peak just above 1000 nm marks the wavelengths the photonic crystal transmits; the suppressed wavelengths lie inside the photonic band gap.

6. Tuning the pillar radius

The position of the band gap is set by the geometry of the lattice. To see this, right-click on the photonic crystal in the device view and choose Mesh editor from the menu (??). The mesh editor (??) lets you change the shape that is repeated to build the crystal — here a tube with a radius of 100 nm, a height of 400 nm, and a chosen number of rings and segments controlling how finely it is meshed.

Right-click context menu on the photonic crystal with the Mesh editor option highlighted. — Right-clicking the photonic crystal opens a context menu. Select **Mesh editor** to change the geometry of the repeated object.

Mesh editor showing a Tube primitive with radius 100 nm, height 400 nm, 10 rings and 32 segments. — The mesh editor with the **Tube** primitive selected. The *Radius* field (here 100 nm) sets the thickness of every pillar in the array.

Device view of the photonic crystal after increasing the pillar radius to 150 nm, showing visibly fatter pillars. — The same photonic crystal after the pillar radius is increased to 150 nm — the pillars are noticeably fatter and pack more dielectric into the lattice.

Change the pillar radius to 150 nm. The pillars become visibly thicker in the device view (??). Re-run the simulation and open lam_norm.csv again to generate the updated transmission spectrum (??).

Next, set the radius to 120 nm and repeat the simulation. The resulting transmission spectrum (??) now peaks near 1200 nm, lying between the original 100 nm result and the 150 nm case. The trend is clear: increasing the pillar radius shifts the photonic bands towards longer wavelengths. By adjusting a single geometric parameter, you can tune the position of the photonic band gap and the wavelengths transmitted by the crystal.

Transmission spectrum for 150 nm pillars, with the main transmission feature shifted to roughly 1400 to 1500 nm. — Transmission for 150 nm pillars. The transmission peak has shifted to approximately 1400–1500 nm, a substantial red-shift relative to the 100 nm structure.

Transmission spectrum for 120 nm pillars, with the main peak near 1200 nm. — Transmission for 120 nm pillars. The peak near 1200 nm lies between the 100 nm and 150 nm results, demonstrating the smooth shift of the photonic bands as the pillar radius increases.

7. Building a photonic crystal waveguide

So far the lattice has been generated for you. To see how, and to take control of it, right-click the photonic crystal and choose Edit object (??). The object editor (??) collects everything about the object: its position, the tube shape, its optical material (here silicon), and — on the Steps row — the rule that stamps the shape out into a lattice. Click the … button on this row to open the step editor, where crystal lattices, repeated structures, and scripted geometries can be created and modified.

Right-click context menu on the photonic crystal with the Edit object option highlighted. — Right-click the photonic crystal and choose **Edit object** to open the full object editor.

Object editor showing object type, offset, the Steps row labelled custom crystal lattice 10x1x10, colour, tube shape, and silicon optical material. — The object editor. The *Steps* row reads “Custom crystal lattice 10x1x10” — the recipe used to repeat the tube and build the crystal. Click the … button at the right of the row to edit it.

Crystal editor showing lattice vectors a1, a2, a3, an origin, and a number of objects of 10 by 1 by 10. — The **Crystal** tab of the step editor. The lattice vectors a1, a2 and a3, together with the object count, define the triangular lattice used to generate the photonic crystal.

Clicking the … button on the Steps row opens the step editor. On the Crystal tab (??) the lattice is defined by three vectors and a count. Here a1 = (400 nm, 0, 0) sets a 400 nm pitch along x, a2 = (0, 1 µm, 0) is the single layer in y, and a3 = (200 nm, 0, 346 nm) offsets each row by half a pitch — a 200 nm shift with a 346 nm = 400 nm × √3/2 spacing — which produces the familiar triangular (hexagonal) close-packed arrangement. The crystal is repeated 10 × 1 × 10 times.

Lua script editor generating the photonic crystal lattice with clear_points and add_point inside two nested for loops, with conditions that skip selected pillars. — The **Lua script** tab. Instead of a regular lattice the positions are generated in code, so any arrangement is possible. The two key commands are `clear_points()` and `add_point()`, and all coordinates are specified in metres.

Device view of a photonic crystal with a U-shaped channel of missing pillars forming a photonic crystal waveguide. — The photonic crystal waveguide. The line of removed pillars forms a U-shaped defect channel. Light whose wavelength lies inside the photonic band gap is confined to the defect and guided around the bend.

Transmission spectrum of the photonic crystal waveguide showing several sharp guided-mode peaks. — Transmission |E_Output|²/|E_Input|² for the waveguide. The multiple sharp peaks are the guided modes of the U-bend channel — wavelengths that are routed around the corner while the rest of the spectrum is blocked.

A regular lattice is the simplest case, but it is far from the only possibility. Click the Lua script button and the editor switches to the scripting view (??). Here the pillar positions are generated programmatically rather than from a predefined crystal lattice. Only two commands are required: clear_points() removes any existing pillar positions, while add_point(x, y, z) adds a new pillar at the specified coordinates. Combined with loops and conditional statements, these commands make it possible to generate almost any photonic crystal geometry.

The example script shown in ?? creates a 13 × 10 lattice with a pitch of 400 nm. A small number of if statements set skip=true for selected pillars, preventing them from being added to the structure. The resulting line of missing pillars forms a defect channel through the crystal. In this example the defect follows a U-shaped path, producing the photonic crystal waveguide shown in ??.

Re-run the simulation and reopen lam_norm.csv. The transmission spectrum of the waveguide (??) now contains several narrow transmission peaks rather than a single broad band. These peaks correspond to guided modes supported by the defect channel within the photonic band gap. Light at these wavelengths is confined to the waveguide and successfully routed around the bend, while wavelengths outside the guided modes are blocked by the surrounding crystal.

Congratulations! You have run a photonic crystal FDTD simulation, measured its transmission spectrum, explored how the photonic bands shift with geometry, and created a working photonic crystal waveguide by introducing a defect into the lattice.

8. The output from FDTD simulation

Each FDTD run produces a collection of outputs that capture different aspects of the optical behaviour — from time snapshots of the field, to the spectra recorded by each detector, to the geometry of the device itself. These files are usually plain csv files which can be opened directly in OghmaNano’s built-in viewers or processed externally (for example, plotting data in Excel or Python). The most important outputs for this photonic crystal study are summarised in Table 1 below.

Table 1: Files produced by the photonic crystal FDTD simulation
File name	Description
detector0/lam_E.csv	Input spectrum \|E\|² vs wavelength (purple detector)
detector1/lam_E.csv	Output spectrum \|E\|² vs wavelength (green detector)
detectorN/lam_norm.csv	Transmission \|E_out\|²/\|E_in\|² vs wavelength
snapshots/	Time snapshots of the field (e.g. `Ey.csv`); see ??
device.csv	3D device / geometry model
escape.csv	Energy escaping the simulation domain
power.dat	Field power vs time
conv.dat	Convergence of the FDTD solver
gui_config.json	Saved view/plot settings; see ??