The effect of external forces on discrete motion within holographic optical tweezers

Holographic optical tweezers is a widely used technique to manipulate the individual positions of optically trapped micron-sized particles in a sample. The trap positions are changed by updating the holographic image displayed on a spatial light modulator. The updating process takes a finite time, resulting in a temporary decrease of the intensity, and thus the stiffness, of the optical trap. We have investigated this change in trap stiffness during the updating process by studying the motion of an optically trapped particle in a fluid flow. We found a highly nonlinear behavior of the change in trap stiffness vs. changes in step size. For step sizes up to approximately 300 nm the trap stiffness is decreasing. Above 300 nm the change in trap stiffness remains constant for all step sizes up to one particle radius. This information is crucial for optical force measurements using holographic optical tweezers

Increasing trap stiffness with position clamping in holographic optical tweezers

We present a holographic optical tweezers system capable of position clamping multiple particles. Moving an optical trap in response to the trapped object's motion is a powerful technique for optical control and force measurement. We have now realised this experimentally using a Boulder Nonlinear Systems Spatial Light Modulator (SLM) with a refresh rate of 203Hz. We obtain a reduction of 44% in the variance of the bead's position, corresponding to an increase in effective trap stiffness of 77%. This reduction relies on the generation of holograms at high speed. We present software capable of calculating holograms in under 1ms using a graphics processor unit. © 2009 Optical Society of America

Two-photon optics of Bessel-Gaussian modes

In this paper we consider geometrical two-photon optics of Bessel-Gaussian modes generated in spontaneous parametric down-conversion of a Gaussian pump beam. We provide a general theoretical expression for the orbital angular momentum (OAM) spectrum and Schmidt number in this basis and show how this may be varied by control over the radial degree of freedom, a continuous parameter in Bessel-Gaussian modes. As a test we first implement a back-projection technique to classically predict, by experiment, the quantum correlations for Bessel-Gaussian modes produced by three holographic masks, a blazed axicon, binary axicon and a binary Bessel function. We then proceed to test the theory on the down-converted photons using the binary Bessel mask. We experimentally quantify the number of usable OAM modes and confirm the theoretical prediction of a flattening in the OAM spectrum and a concomitant increase in the OAM bandwidth. The results have implications for the control of dimensionality in quantum states.Comment: 8 pages, 10 figure

Violation of Leggett inequalities in orbital angular momentum subspaces

We report an experimental test of Leggett's non-local hidden variable theory in an orbital angular momentum (OAM) state space of light. We show that the correlations we observe are in conflict with Leggett's model, thus excluding a particular class of non-local hidden variable theories for the first time in a non-polarization state space. It is known that the violation of the Leggett inequality becomes stronger as more detection settings are used. The required measurements become feasible in an OAM subspace, and we demonstrate this by testing the inequality using three and four settings. We observe excellent agreement with quantum predictions and a violation of five and six standard deviations, respectively, compared to Leggett's non-local hidden variable theory

Perceptions of Leading and Supporting School and District Leaders Through a Personalized Learning Initiative in the Southeastern United States

Background: Student achievement through standardized assessments have measured how students are performing in school. According to sources of data, there is an achievement gap that occurs with many subgroups including students of color, with disabilities, as well as socioeconomic status. As a result, personalized learning was conceptualized to help meet students’ individual needs and interests to increase student achievement outcomes. Purpose: The purpose of this qualitative study is to gain a greater understanding of personalized learning implementation based on the perspectives of those who have been involved in the process. Literature Review: The literature review is a synthesis of the history and politics of student achievement in the K-12 public educational setting, provides an overview of personalized learning, examines the theoretical framework of instructional leadership as well as leading personalized learning. Research Design: To help address the essence of personalized learning and to gain a deeper understanding of this qualitative research study, a case study was utilized. Data Collection and Analysis: Semi-structured interviews with 9 participants and an analysis of the themes was used to gain a greater understanding of the effects of implementation of personalized learning. Results: Based on the interviews with teachers, district leaders, and school leaders, several themes emerged after analyzing the data gathered. The three themes were identified as: implementation impacted outcomes; monitoring influenced implementation and outcomes; and prioritization of personalized learning varied. Conclusion: As school and district leaders consider adopting personalized learning, or even other instructional initiatives, creating a level of uniformity with implementation and defining how the initiative will be monitored are recommendations that should be considered. Additionally, future research is needed to help school and district leaders understand the successes and challenges of implementing personalized learning

The transition from a coherent optical vortex to a Rankine vortex: beam contrast dependence on topological charge

Spatially coherent helically phased light beams carry orbital angular momentum (OAM) and contain phase singularities at their centre. Destructive interference at the position of the phase singularity means the intensity at this point is necessarily zero, which results in a high contrast between the centre and the surrounding annular intensity distribution. Beams of reduced spatial coherence yet still carrying OAM have previously been referred to as Rankine vortices. Such beams no longer possess zero intensity at their centre, exhibiting a contrast that decreases as their spatial coherence is reduced. In this work, we study the contrast of a vortex beam as a function of its spatial coherence and topological charge. We show that beams carrying higher values of topological charge display a radial intensity contrast that is more resilient to a reduction in spatial coherence of the source

Heralded phase-contrast imaging using an orbital angular momentum phase-filter

We utilise the position and orbital angular momentum (OAM) correlations between the signal and idler photons generated in the down-conversion process to obtain ghost images of a phase object. By using an OAM phase filter, which is non-local with respect to the object, the images exhibit isotropic edge-enhancement. This imaging technique is the first demonstration of a full-field, phase-contrast imaging system with non-local edge enhancement, and enables imaging of phase objects using significantly fewer photons than standard phase-contrast imaging techniques

Holographic tracking and sizing of optically trapped microprobes in diamond anvil cells

We demonstrate that Digital Holographic Microscopy can be used for accurate 3D tracking and sizing of a colloidal probe trapped in a diamond anvil cell (DAC). Polystyrene beads were optically trapped in water up to Gigapascal pressures while simultaneously recording in-line holograms at 1 KHz frame rate. Using Lorenz-Mie scattering theory to fit interference patterns, we detected a 10% shrinking in the bead’s radius due to the high applied pressure. Accurate bead sizing is crucial for obtaining reliable viscosity measurements and provides a convenient optical tool for the determination of the bulk modulus of probe material. Our technique may provide a new method for pressure measurements inside a DAC

Experimental high-dimensional two-photon entanglement and violations of generalised Bell inequalities

Quantum entanglement plays a vital role in many quantum information and communication tasks. Entangled states of higher dimensional systems are of great interest due to the extended possibilities they provide. For example, they allow the realisation of new types of quantum information schemes that can offer higher information-density coding and greater resilience to errors than can be achieved with entangled two-dimensional systems. Closing the detection loophole in Bell test experiments is also more experimentally feasible when higher dimensional entangled systems are used. We have measured previously untested correlations between two photons to experimentally demonstrate high-dimensional entangled states. We obtain violations of Bell-type inequalities generalised to d-dimensional systems with up to d = 12. Furthermore, the violations are strong enough to indicate genuine 11-dimensional entanglement. Our experiments use photons entangled in orbital angular momentum (OAM), generated through spontaneous parametric down-conversion (SPDC), and manipulated using computer controlled holograms