Niet-lineaire vibratie spectroscopiën van biomoleculaire systemen

Er is recent veel vooruitgang geboekt in de ontwikkeling van niet-lineaire vibratie spectroscopische methoden voor onderzoek van biologische macromoleculaire systemen(1,2,3,4). De niet lineaire vibratie spectroscopische technieken die in onze groep in gebruik en in ontwikkeling zijn, zijn CARS (coherente anti-Stokes Raman verstrooiing), stRg (gestimuleerde Raman verstrooiing), IR/V-SFG (infrarood-zichtbaar licht som frequentie generatie). Daarnaast wordt gebruik gemaakt van niet-lineaire optische eigenschappen van materie, zoals parametrische fluorescentie, verschil frequentie generatie en tweede harmonische generatie, om laser emissie met geschikte karakteristieken te genereren. Als standaard techniek zijn in de groep zeer geavanceerde Raman microspectrometers voor spontane Raman verstrooiing (spR) beschikbaar. Het doel van het onderzoek is om gevoelige methoden te ontwikkelen voor detectie van kleine aantallen molekulen, bijvoorbeeld aan oppevlakken en in biologische cellen. We richten ons op de vibratie selectieve technieken omdat: 1) vibraties niet alleen geschikt zijn voor detectie maar ook voor identificatie, 2) vibraties zijn gevoelig voor inter- en intramolekulaire interacties, 3) vibraties kunnen helpen bij het bepalen van de molekulaire orientatie of de relatieve orientatie van molekulen en 4) vibraties maken het mogelijk om zeer snelle dynamica in materie te bestuderen. In het bijzonder niet-lineaire optische technieken zijn interessant vanwege: a) spectrale scheiding tussen fluorescentie en signaal (bijvoorbeeld in CARS en IR/V-SFG), b) gecollimeerde signaal bundel maakt efficiente signaal collectie mogelijk, c) hoge signaal niveaus door gebruik te maken van gestimuleerde verstrooiings processen (CARS, stRg) en/of door resonantie (IR/V-SFG), d) efficiente belichting door gecollimeerde lichtbundels, waardoor combinaties met golfgeleiders mogelijk zijn (CARS, stRg en spR) en oppervlakte gevoeligheid ontstaat door evanescente veld excitatie of intrinsieke eigenschappen van c(2) (IR/V-SFG).\ud Na een korte inleiding worden in het vervolg resultaten gepresenteerd van polarisatiegevoelige multiplex CARS, golfgeleider Raman verstrooiing en een optisch parametrische oscillator. Deze vormt het hart van een IR/V-SFG spectrometer die in ontwikkeling is

An inverse method for color uniformity in white LED spotlights

Color over Angle (CoA) variation in the light output of white phosphor-converted LEDs is a common problem in LED lighting technology. In this article we propose an inverse method to design an optical element that eliminates the color variation for a point light source. The method in this article is an improved version of an earlier method by the same authors, and provides more design freedom than the original method. We derive a mathematical model for color mixing in a collimator and present a numerical algorithm to solve it. We verify the results using Monte-Carlo ray tracing

A least-squares method for optimal transport using the Monge-Ampère equation

In this article we introduce a novel numerical method to solve the problem of optimal transport and the related elliptic Monge--Ampère equation. It is one of the few numerical algorithms capable of solving this problem efficiently with the proper transport boundary condition. The computation time scales well with the grid size and has the additional advantage that the target domain may be nonconvex. We present the method and several numerical experiments

Broadband multiple light scattering in white LED diffusers

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

An inverse method for the design of TIR collimators to achieve a uniform color light beam

Color over Angle (CoA) variation in the light output of white LEDs is a common and unsolved problem. In this article we introduce a new method to reduce CoA variation using a special collimator. The method is based on analytical inverse design methods. We present a numerical algorithm to solve the di¿erential equations arising from this method and verify the results using Monte-Carlo raytracing

A least-squares method for optimal transport using the Monge-Ampère equation

In this article we introduce a novel numerical method to solve the problem of optimal mass transport and the related elliptic Monge-Ampère equation. It is one of the few numerical algorithms capable of solving this problem efficiently with the proper boundary conditions. It scales well with the grid size and has the additional advantage that the target domain may be non-convex. We present the method and several numerical experiments

Existence and uniqueness of solutions to Liouville's equation and the associated flow for Hamiltonians of bounded variation

We prove existence and uniqueness for solutions to Liouville's equation for Hamiltonians of bounded variation. These solutions can be interpreted as the limit of a sequence generated by a series of smooth approximations to the Hamiltonian. This results in a converging sequence of approximations of solutions to Liouville's equation. As an added perk, our method allows us to prove a generalisation of Liouville's theorem for Hamiltonians of bounded variation. Furthermore, we prove there exists a unique flow solution to the Hamilton equations and show how this can be used to construct a solution to Liouville's equation. Key words: partial differential equations, geometrical optics, Liouville's equation, flow

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