The Beer-Lambert-Bouguer absorption law, known as Beer's law for absorption in an optical medium, is precise only at power densities lower than a few kW. At higher power densities this law fails because it neglects the processes of stimulated emission and spontaneous emission. In previous models that considered those processes, an analytical expression for the absorption law could not be obtained. We show here that by utilizing the Lambert W-function, the two-level energy rate equation model is solved analytically, and this leads into a general absorption law that is exact because it accounts for absorption as well as stimulated and spontaneous emission. The general absorption law reduces to Beer's law at low power densities. A criterion for its application is given along with experimental examples.

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A cw singly resonant optical parametric oscillator (SRO) was built and placed inside the cavity of a ring laser. The system consists of a diode-end-pumped Nd:YVO4 ring laser with intracavity periodically poled lithium niobate as the nonlinear gain medium of the SRO. When the laser was operated in a unidirectional mode, we obtained more than 520 mW of signal power in one beam. When the laser was operated in a bidirectional mode, we obtained 600 mW of signal power (300 mW in two separate beams). The power and the spectral features of the laser in the unidirectional and bidirectional modes were measured while the laser was coupled with the SRO. The results show that it is preferable to couple a SRO with a unidirectional ring laser.

Developments in theoretical investigations and experimental techniques are reaching a level of maturity for which it is finally becoming possible to answer some of the most pressing questions in turbulence. The prevailing classical theories all have their strengths and drawbacks based on their respective principal assumptions. To better understand the implications of these assumptions, we have developed a theoryintensive experimental strategy. For these purposes, a laboratory has been established at the Department of Mechanical Engineering, Technical University of Denmark. The objective being to provide the data necessary to test the (bounds of) validity of the existing theories; Most prominently the classical Richardson-Kolmogorov-Batchelor paradigm, but also other generally adopted views such as Rapid Distortion Theory and Equilibrium Similarity. The measurements will be analyzed within a novel theoretical framework that enables not only quantification of the degree to which the small and intermediate scale turbulence behaves according to the existing theories (and their central assumptions), but also unveiling the underlying processes that create the respective state of turbulent flow. The present work will describe the current state of the developments of building up the laboratory.

Measurements of 3D volumetric velocity fields are of great theoretical interest with numerous practical applications. These measurements are essential for studying volumetric flows that do not exhibit inherent flow symmetry, such as turbulence or vortex breakdown. In the past decade, several technological innovations facilitated the emergence of 3D-PTV techniques for measuring velocity fields at kHz rate with volumes of interest up to 104 cm3 that contain 300 µm helium-filled soap bubbles. However, when a commercial laser beam with millijoule pulse-energy is expanded and shaped to fill volumes above 102 cm3 for 3D-PTV experiments with 15 µm air filled soap bubbles, one finds that the power density of the laser source is insufficient to generate a signal image. This is because the power density of the laser beam falls inversely with respect to its cross-section area and due to the quadratic dependence of Mie-scattering on the particle diameter. Here, we report of the analysis and development of two optical techniques for extending the volume of measurement in volumetric PTV. In particular, when a volume about 103 cm3 is seeded with 15 µm air-filled soap bubbles and a laser with a pulse energy of few single mJ illuminates it. The first technique uses multi reflections between two opposing parallel mirrors. The second technique is a development of laser scanning PIV for volumetric scanning: The potential to increase the scanned volume is examined by experimenting with an acousto-optic modulator for fast scanning. Furthermore, by employing an off-axis parabolic mirror, we obtain parallel beam scanning, which increases the efficiency and quality of the scanning.