"We were positively surprised that you could apply fundamental physics to describe these systems," says Willem Vos of the University of Twente. "The lighting industry was relying on simulations to see how light propagates through a medium, but with simulations you don’t get insights just numbers – we wanted to get insights."

Until now, lighting engineers have had to guess critical parameters and then run ray-tracing simulations to see if they produce the desired effect. By combining diffusion theory analysis with experiments on industrial LEDs, the researchers were instead able to establish a physics-based connection between the density of the phosphors used in an LED and the optical properties of the light produced. Their systematic investigations also suggest why the ceramic phosphor exploited in many industrial LEDs has proved so successful, something that until now had not been fully understood. "This work will help people to reach a solution more quickly," added Vos.

Applying first principles

Philips approached Vos and his team at the University of Twente Institute of Nanotechnology explaining that they had white LEDs that worked but that no-one really knew how.

Most industrial white LEDs are produced by adding phosphors to a blue-emitting semiconductor diode. These trigger a series of energy transfer and scattering processes when light is emitted from the diode resulting in diffuse white light. The phosphor layer must be carefully designed to achieve even lighting with no angular colour distribution, and to ensure multiple scattering within thinner, and hence cheaper, layers.

By analysing the diffusion theory equations describing how light interacts with the phosphorescent material in LEDs, the researchers were able to determine key optical properties such as the total transmission, and the mean free path length for the absorption and transport of light. They also experimentally measured the spectra and intensity of the transmission when white light was shone on polymer plates containing a phosphorescent material typically used in LEDs produced by Philips. These materials use YAG:Ce3+, among the most commonly used compounds for phosphors.

Insights not numbers

They found that phosphor densities that yield an absorption-free path length of around the thickness of the phosphor layer yield the optimal properties for white diffuse light.

They also calculated the ratio of scattered to absorbed light in the phosphorescent material, a measure known as the "albedo". Complex photonic media typically have a very high albedo, greater than 0.98, but for these materials Vos and his colleagues calculated a surprisingly low albedo of 0.7, regardless of the phosphor density. "It is well known in the trade that these are favourable phosphors and now we know why," he added.

Vos and his team mapped the output from systems with different phosphor densities onto the mathematically defined colour spaces exploited by engineers to compare lighting systems. The researchers also found a way to predict how this positioning was affected by the phosphor density on the basis of the mean-free path lengths of transport and diffusion.

Next steps

"We’ve still only just begun with our work on these systems," said Vos. Next they will turn their attention to "artificial" lighting systems composed of well understood materials, which will enable them to investigate how effectively these systems can be customized with more informed design.

"It’s a really exciting time for the industry," he added. "The industry is learning new systems, which has rejuvenated it and is attracting young people into the lighting trade."

Full details are reported in Optics Express.