# Why are Photonics Researchers Embracing FEM?

The Finite Element Method (FEM) is a popular tool used by engineers to reduce the number of prototypes and virtual experiments necessary to create a successful design. It uses complex mathematics to create virtual simulations that can realistically test the integrity of a design.

As discussed in a previous post, FEM is a numerical solution for a complex problem, which is used to create simulations. These simulations break down a large problem into a mesh of smaller elements that help researchers understand how all the minute details of a design are working together, which saves them time and money. In the past, FEM was predominantly used by engineers to test the potential of physical designs, but today it is used for much more.

#### What is the history of the Finite Element Method?

While FEM is a relatively modern invention, its roots go back to the 18th Century mathematician Leonhard Euler, who invented a method for solving ordinary differential equations with a given initial value. In the 1940s, engineer Alexander Hrennikoff and mathematician Richard Courant would build off of this method to perfect what is now considered FEM. As Trevor English in Interesting Engineering reports, the method was largely used in the 1950s to create designs for civil engineering and aerospace. Eventually, it would also be used to solve problems for computational fluid dynamics. It wasn’t until the 1990s, however, that the technology had enough computing ability to receive more widespread use. At that time, it began to expand to vehicle manufacturers, who used it to make more aerodynamic cars. Engineers that study computational fluid dynamics (CFD), a branch of fluid mechanics, also began to use it.

“For many modern engineers, understanding the complex mathematics behind CFD isn’t necessary to run simulations,” writes English. “The tools are not only being used by experts in fluid dynamics and mathematics, but they can also now be accessed by the everyday engineer having virtually any skill level.”

#### Photonics Researchers Embrace FEM

More recently, photonics engineers have begun embracing FEM to test their research and designs. Whereas FEM traditionally is used to test physical designs, it takes on a different role in photonics research, according to Dr. Arti Agrawal. Dr. Agrawal is a professor at the School of Electrical and Data Engineering at the City University of London, an IEEE Photonics Society Member, and author of the book, “Finite Element Modeling Methods for Photonics.”

“We want to know how the electric field and the magnetic field will change if the refractive index changes, what about the continuity of the field?” she said.

Some photonics researchers are already using FEM to make important discoveries, including research that sheds light on a new way to create low-threshold, surface-emitting laser diodes that span between the ultraviolet to deep visible range.

“Our studies open a new paradigm for developing low-threshold surface-emitting laser diodes from the ultraviolet to the deep visible (~200 to 600 nm), wherein the device performance is no longer limited by the lack of high-quality [distributed Bragg reflectors] DBRs, large lattice mismatch, and substrate availability,” the authors wrote in Science Advances.

FEM may be a new solution in the world of optics. However, it is already demonstrating a lot of promise.

#### Finite Element Method (FEM) for Photonics

Learn how FEM can be used to model and simulate photonic components/devices and analyze how they will behave in response to various outside influences. The Finite Element Method for Photonics course program, created by Dr. Agrawal, provides a comprehensive and up-to-date account of FEM in photonics devices, with an emphasis on practical, problem-solving applications and real-world examples. Engineers will gain an understanding of how mathematical concepts translate to computer code finite element-based methods after completing this program.

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

English, Trevor. (7 November 2021). What Is Finite Element Analysis and How Does It Work? Interesting Engineering.

Ra. Yong-Ho. Tonny Rashid, Roksana, Liu, Xianhe, Sadaf, Sharif, Mashooq, Kishwar, and Mi, Zetian. (3 January 2020). An electrically pumped surface-emitting semiconductor green laser. Science Advances.