How the Finite Element Method (FEM) Enhances Optical Lens Design and Analysis 


Optical lenses are vital components to the manufacturing and labeling of goods. For example, optical lenses are found in electronic devices like smartphones and laptops. They’re also used to make logos and graphics on hardware as well as other kinds of markings commonly found on commercial products and food packaging. These markings are created by high-powered lasers that pass through a series of optical lenses. 

Computer simulation technology is important to the development of optical lenses, because it can reduce the number of prototypes needed during the design phase. These simulations give developers valuable insight into how to improve optical lens designs while also saving time.

There are a few simulation methods that can be used to analyze lens designs, from traditional techniques to those that solve all of Maxwell’s equations—a sophisticated set of equations that describe how electric charges and electric currents produce electric and magnetic fields.

Optical lens simulation relies on two categories. The first is design, in which a lens is optimized specifically for a certain function. The second is analysis, which gives a designer insight into what’s happening within the lens. 

“Wave Optics” for Design

An example of optical lens design is the process of determining the ideal shape for a lens to direct a laser in a particular way. Typically, the goal of lens design is to reduce abnormalities as much as possible. 

Simulations that employ ray-tracing, a process in which rays approximate electromagnetic waves, are often used for design. However, ray-tracing simulations don’t provide the effects of diffraction, which is characterized by light slightly bending as it passes over the edge of an object, so they aren’t 100% effective. In situations where it’s necessary to capture diffraction, “wave-optics” methods are considered ideal. These are computational high-frequency electromagnetics software that rely on a number of general-purpose numerical methods, including the finite-element methods (FEM). As discussed in a previous post, FEM is a numerical solution that breaks down a much larger, complex problem into a series of smaller ones (“finite elements”) in order to make the overall problem easier to examine. This equation is then used to create a simulation (known as the finite element analysis), which gives engineers a more detailed look into the design and how its various elements work together. 

Unlike other methods, wave optics can be used for both design and analysis of optical lenses. 

“Wave Optics” for Analysis

For optical lens analysis, Maxwell’s equations are necessary to acquire the electromagnetic fields’ complete vector representation. A simulation method known as “full-wave” uses FEM to solve the entire domain of Maxwell’s equations by breaking it down into a mesh. It is then subdivided into smaller elements with a simpler shape. 

The full-wave method poses some challenges. For example, the innumerable mesh elements created can be difficult for a typical computer to handle. However, there are formulations to get around this issue.

Full-wave simulations for multicomponent optical systems were once thought impossible, but thanks to these FEM-based methods, the ability to simulate whole optical systems is closer than ever before. 

Finite Element Method (FEM) for Photonics





Mizuyama, Yosuke. (15 September 2020). Full-wave simulation extends the range and depth of lens analysis. Laser Focus World. 

Sjodin, Bjorn. (9 November 2017). Wave Optics: Beam-envelope method efficiently analyzes photonic components. Laser Focus World. 

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