Teus W. Tukker

Broadband mean free path of diffuse light in polydisperse ensembles of scatterers for white light-emitting diode lighting

We study the diffuse transport of light through polymer slabs containing TiO(2) scattering particles. The slabs are diffuser plates typical of a commercial white light-emitting diode (LED) module (Fortimo). We have measured the diffuse transmission and reflection properties over a broad wavelength range (470-840 nm) from which we derive the transport mean free path using the theory of light diffusion. With increasing scatterer density, the mean free path becomes shorter. The mean free path increases with wavelength; hence, blue light is scattered more strongly than red light. To interpret the results, we propose an ab initio model without adjustable parameters for the mean free path by using Mie theory. We include inhomogeneous broadening as a result of the size distribution of the scattering particles as measured by dynamic light scattering. Surprisingly, the calculated mean free path decreases with wavelength, at variance with our experiments, which is caused by particles with radii R in excess of 0.25 μm. Close inspection of the scatterers by electron microscopy reveals that large particles (R>0.4 μm) consist of clusters of small particles (R<0.13 μm). Therefore, we have improved our model by only taking into account the individual scatterers within the clusters. This model predicts mean free paths in good agreement with our experimental results. We discuss consequences of our results to white LED lighting modules.

A Monge-Ampère-solver for free-form reflector design

In this article we present a method for the design of fully free-form reflectors for illumination systems. We derive an elliptic partial differential equation of the Monge--Ampere type for the surface of a reflector that converts an arbitrary parallel beam of light into a desired intensity output pattern. The differential equation has an unusual boundary condition known as the transport boundary condition. We find a convex or concave solution to the equation using a state of the art numerical method. The method uses a nonstandard discretization based on the diagonalization of the Hessian. The discretized system is solved using standard Newton iteration. The method was tested for a circular beam with uniform intensity, a street light, and a uniform beam that is transformed into a famous Dutch painting. The reflectors were verified using commercial ray tracing software.

Variable liquid lenses for electronic products

The design, manufacturing and application of variable liquid lenses are discussed. The interface between the two immiscible liquids that forms the lens can be altered with a voltage. Results are presented of applying this lens in miniature autofocus and zoom cameras, in optical recording and in illumination systems.

Beam-shaping lenses in illumination optics

Beam-shaping optics are used in various optical fields to change the luminous intensity distribution. In this paper a flexible method is presented to design beam-shaping optics with aspherical surfaces transforming the intensity profile of the light beam into any desired profile. The method is applied to a collimator lens that transforms a beam from a Lambertian emitter to a uniform light distribution.

A Novel Scheme for Liouville's Equation with a Discontinuous Hamiltonian and Applications to Geometrical Optics

A novel scheme is developed that computes numerical solutions of Liouville’s equation with a discontinuous Hamiltonian. It is assumed that the underlying Hamiltonian system has well-defined behaviour even when the Hamiltonian is discontinuous. In the case of geometrical optics such a discontinuity yields the familiar Snell’s law or the law of specular reflection. Solutions to Liouville’s equation should be constant along curves defined by the Hamiltonian system when the right-hand side is zero, i.e., no absorption or collisions. This consideration allows us to derive a new jump condition, enabling us to construct a first-order accurate scheme. Essentially, the correct physics is built into the solver. The scheme is tested in a two-dimensional optical setting with two test cases, the first using a single jump in the refractive index and the second a compound parabolic concentrator. For these two situations, the scheme outperforms the more conventional method of Monte Carlo ray tracing.

Transport of light through white-LED phosphor plates

Energy efficient generation of white light has become an important societal issue in recent years. The technology of white-light emitting diodes (LEDs) is one of the main directions (Akasaki I, Amano H, Nakamura S, Blue LEDs – filling the world with new light, http://www.nobelprize.org/, 2014; Schubert EF, Light emitting diodes. Cambridge: Cambridge University, 2006). Key challenges in the white LED usage are understanding scattering, absorption and emission from ab-initio, and extracting the transport properties in the region where both emission and absorption overlap. Physical understanding of multiple light scattering in the LED provides tools to extract optical parameters of this system, and greatly simplify the LED design process. In this work we have been able to measure the total transmission, using a novel technique, in the region where emission and absorption overlap, and to extract transport parameters in the whole visible range.

Broadband multiple light scattering in white LED diffusers

Summary form only given. There is a strong worldwide drive to efficient general lighting using white light emitting diodes (LEDs) [1,2]. White LEDs often consist of a semiconductor diode [3,4,5] combined with luminescent phosphors [5] to convert part of the blue light to green yellow, and red. In state-of-the art white-light LEDs one exploits multiple scattering of light [1,2]. The transport of light then becomes diffusive, which serves to obtain a desirable smooth lighting without hot spots and without angular color distribution. Moreover, photons are recycled so that thin phosphor layers serve to improve cost efficiency and reduce environmental impact.Central challenges in the understanding of white LEDs arise from limitations in the physical understanding of the combined multiple light scattering and energy conversion in phosphors. LEDs are currently described by raytracing and Monte Carlo techniques [1,2]. Unfortunately, LED spectra cannot be predicted quantitatively, as optical parameters must be adjusted to be inconsistent with other data. These limitations hamper the design and development of efficient white LEDs. An improved description of multiple light scattering could be obtained by analytical theories originating from nanophotonics, invoking detailed nanostructure of a sample. We have measured diffuse optical transmission and reflectivity through diffuser plates typical of a commercial white LED (Fortimo). Using photonic diffusion theory we derive the transport mean free path [6-8]. With increasing scatterer density the mean free path decreases. To interpret the results, we use an ab initio model without free parameters by combining Mie theory with known properties, such as the scatterer size distribution taken from SEM. Our model predicts mean free paths in dramatically improved agreement with our data, without adjustable parameters [9]. We will discuss consequences for light scattering in white lighting modules.

Efficient collimator design for extended light sources with the flux tube method

In the last years it has been shown that efficient collimator systems for point sources can be designed with the flux tube method in combination with an optimiser. In this paper it will be shown that this method can be extended to extended light sources. Various collimator designs for different types of sources will be discussed that transform the illuminance into imposed distribution.

Photo Replication of Birefringent Phase Structures

Dual layer blu-ray disc (BD) and dual layer small form factor optical drive (SFFO) as well as BD / digital versatile disc (DVD) / compact disc (CD) compatible systems, require phase structures to cope with the different amount of spherical aberration for the various different operating modes. Birefringent phase structures open up to the possibility to cope with these different amounts of aberration in the various readout modes, but so far no manufacturing methods are known which lead to low cost and stable structures. A novel replication method, based on the photo-polymerization of a liquid crystalline monomer is presented to make birefringent phase structures. Apart from enabling mass production, the process allows a phase structure to be directly produced on top of an ordinary objective lens, allowing weight and size reduction of the compatible optical pick up.