# What Method Should Photonics Engineers Use for Optical Simulations?

Photonics engineers rely on optical simulations for their designs. Depending on the optical size of their model geometry, they need to choose the best method for performing these simulations, according to Christopher Boucher, a lead developer at COMSOL, a simulation software.

“The concept of optical size is essential to choosing a formulation for numerical simulation of electromagnetic waves,” Boucher writes in Laser Focus World. “Engineers working with simulation are constantly tasked with balancing accuracy against computational cost; we try to produce a model that best represents real-world behavior, but it must be within the time constraints of our assignment and with the limited computational resources at hand.”

If your simulation domain is only a few wavelengths across, Boucher recommends the finite element method as ideal. However, if it encompasses “a large number of wavelengths,” he says you will want to use the ray tracing method.

How should you use these methods to perform optical simulations? Here is what Boucher recommends:

#### Finite Element Method (FEM)

Using FEM, the model geometry is broken down into small mesh elements, in which equations are solved numerically. One way to model electromagnetic waves is through the “full-wave” method. It directly solves Maxwell’s equations for the electric field and accurately represents real-world phenomena without making too many simplifying assumptions.

“It can faithfully reproduce wavelength-scale behaviors such as diffraction and interference, which significantly impact the operation of nanophotonic devices,” writes Boucher.

However, he notes one problem with this approach. “The mesh must be fine enough to resolve individual oscillations of the electric field, so the simulations require more time and RAM to solve as the geometry size is increased. Therefore, this method is best suited for a model geometry that does not exceed a few wavelengths in all directions.”

#### Ray Tracing

Rather than solving individual waves on a very fine mesh, the ray tracing method  represents “light as rays that can reflect and refract at boundaries between different media,” according to Boucher. However, he notes that this approach usually neglects wavelength-scale phenomena such as diffraction.

#### Other solutions

While FEM and ray tracing are adequate methods for many optical simulations, other methods may work better for complex problems. For example, if the geometry has one dimension that is comparable to the wavelength, but another dimension that is much longer, the beam envelope method may be preferable. According to Boucher, this method is “best suited for systems in which waves are constrained to propagate in one or two known directions, including in cables and directional couplers.”

Beginning with the full-wave solution, “in which the instantaneous electric field amplitude is resolved over each wavelength,” you can apply “a clever change of variables and instead solve for the amplitude of a slowly varying amplitude function,” which “relaxes the requirement from full-wave FEM that the mesh elements must be small enough to resolve individual wavelengths,” he explains.

Performing optical simulations can be a complex process. However, determining the best method based on your model’s geometry can simplify the process and lead to more successful outcomes.

#### Learn the Finite Element Method (FEM)

The new course program from IEEE Educational Activities provides a comprehensive and up-to-date account of FEM in photonics devices. Finite Element Method for Photonics has an emphasis on practical, problem-solving applications and real-world examples. Engineers will come away with an understanding of how mathematical concepts translate to computer code finite element-based methods.

Connect with an IEEE Content Specialist today to learn how to get access to this program for your organization.

Interested in the course for yourself? Visit the IEEE Learning Network (ILN).

#### Resources

Boucher, Christopher. (16 August 2021). Multiscale optical simulations pose unique challenges. Laser Focus World.