Question

Class project:

Pick a topic related to work or personal and show how you implement Project Management (PMI ) techniques such as  initiating, planning, executing, monitoring and controlling. Your paper should include as relevant PMI concepts such  

Work Breakdown Structure (WBS)

Gantt Charts

Critical Path Method (CPM)

Waterfall / Linear

Kanban

. Typical Sections of Your Paper.

Sections	Definitions
Abstract	Purpose, scope, principle results and conclusions
Introduction	Problem or issue, background, and reason for the study
Text Body	Methodology, analysis, or other value added process
Conclusions	Summary in layman's terms of the result of this study
Recommendations	Specific steps to follow as a result of this study
Acknowledgements	Note funding support and/or other assistance
References	Published sources of information used in support of this study

The length of the paper could anywhere from 2 pages to maximum of 10 pages

Answer 1

Project topic : Optical Tweezers

Abstract :

In this project report the concept of optical tweezers and its applications have been presented. Optical tweezers, tools based on strongly focused light, enable optical trapping, manipulation, and characterisation of a wide range of microscopic and nanoscopic materials. In the limiting cases of spherical particles either much smaller or much larger than the trapping wavelength, the force in optical tweezers separates into a conservative gradient force, which is proportional to the light intensity gradient and responsible for trapping, and a non-conservative scattering force, which is proportional to the light intensity and is generally detrimental for trapping, but fundamental for optical manipulation and laser cooling. Here, after an introduction to the theory and practice of optical forces, an overview of few recent applications to different fields is given.

Introduction :

Optical tweezers which are also known as single-beam gradient force trap actually are scientific instruments which can hold or move microscopic objects like atoms, nano droplets, nanoparticles with the use of a highly focused laser beam. In lab we use tweezers to interact with macroscopic objects, optical tweezers are in a manner similar to those tweezers, the only difference is it can interact with microscopic objects like DNA molecules, cells, nano particles. Optical tweezers harness the photon pressure produced by an intense beam of laser light to hold and manipulate micrometer-sized particles. Each photon of light carries energy hν and momentum hν/c, so if absorbed by an object the momentum transferred from a light beam of power P gives a reaction force F on the object is nP/c.

Optical tweezers work by arranging the direction and intensity of the incoming beams of light to be such that the object is held fixed in three dimensions. One might imagine that this would require a very complicated optical arrangement. However all that is required is a high numerical aperture lens and an input beam of Gaussian intensity profile. A microscope objective lens and a laser pointer of a few milliwatts power output is all that is required to capture and manipulate micrometer-sized glass or plastic beads suspended in water, which was first designed by Arthur Ashkin (2018 Nobel laureate)

-dP1 -dP2 dP1 dP dP2 P1 P2 Fig. 1 Qualitative picture of the origin of the trapping force. The deflection of photons caused by a difference in the index of refraction transfers a net momentum on the microbead, which causes a restoring force back to the focus of the laser beam. Two photon paths, p1 and p2, are compared. The momentum balance dp = dpi – dpf for two beam paths is depicted in green, and shows that for a microbead that is slightly off the optical axis, a net restoring force, caused by dpx, back to the center of the trap is generated.

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Trapping mechanism :

Optical trapping is based on the transfer of momentum from photons to a transparent object immersed in a medium with a different refractive index. High photon-flux sources like lasers can provide sufficient momentum transfer to manipulate micro-sized polystyrene or silica spheres. A stable optical trap requires a potential minimum, such that a small excursion results in a restoring force back to the center of the trap. In order to understand this idea, it is illustrative to separate the effect of the momentum transfer of photons into two components: the gradient force, which attracts the microbead toward the focus (Fig. 1), and the scattering force, which acts in the direction of light propagation. In most cases the scattering force will dominate over the gradient force. If, however, the laser beam is tightly focused, the intensity gradient around the laser focus becomes steep. In such a situation, close to the tight focus, the gradient force component surpasses the scattering force, which leads to a stable optical trap. Using micron-sized beads, optical traps with a spring constant on the order of 102 pN/μm can be generated with a tightly focused laser beam of around 1 W.  

Most optical traps operate with a Gaussian beam (TEM00 mode) profile intensity. In this case, if the particle is displaced from the center of the beam, as in the right part of the figure, the particle has a net force returning it to the center of the trap because more intense beams impart a larger momentum change towards the center of the trap than less intense beams, which impart a smaller momentum change away from the trap center. The net momentum change, or force, returns the particle to the trap center. If the particle is located at the center of the beam, then individual rays of light are refracting through the particle symmetrically, resulting in no net lateral force. The net force in this case is along the axial direction of the trap, which cancels out the scattering force of the laser light. The cancellation of this axial gradient force with the scattering force is what causes the bead to be stably trapped slightly downstream of the beam waist.

Electric dipole approximation :

In cases where the diameter of a trapped particle is significantly smaller than the wavelength of light, the conditions for Rayleigh scattering are satisfied and the particle can be treated as a point dipole in an inhomogeneous electromagnetic field. The force applied on a single charge in an electromagnetic field is known as the Lorentz force,

$F_1=q(E_1+\frac{dx_1}{\mathrm{d} t}\times B)$

$F_2=q(E_2+\frac{dx_2}{\mathrm{d} t}\times B)$

The force on the dipole can be calculated by substituting two terms for the electric field in the equation above, one for each charge. The polarization of a dipole is ? = ?? where ? is the distance between the two charges. For a point dipole, the distance is infinitesimal, . Taking into account that the two charges have opposite signs, the force takes the form

(21 - 22

$F=q(E_1-E_2+\frac{d(x_1-x_2)}{\mathrm{d} t}\times B)$

If ? be the resultant field and ? be the polarization then above equation reduces to,

$F=\epsilon_0 \chi(\frac{1}{2}\triangledown E^2+\frac{\partial (E\times B) }{\partial t})$

The second term in the last equality is the time derivative of a quantity that is related through a multiplicative constant to the Poynting vector, which describes the power per unit area passing through a surface. Since the power of the laser is constant when sampling over frequencies much shorter than the frequency of the laser's light, the derivative of this term averages to zero and the force can be written as

$F=\frac{1}{2}\epsilon_0 \chi \triangledown E^2=\frac{2\pi n_1a^3}{c} (\frac{n_1^2-n_0^2}{n_1^2+2n_0^2}) \triangledown E^2$

Where $n_1$ and $n_0$ are the refractive indices of the nanoparticleand the surrounding medium respectively. ? is the radius of the nanoparticle. The square of the magnitude of the electric field is equal to the intensity of the beam as a function of position. Therefore, the result indicates that the force on the dielectric particle, when treated as a point dipole, is proportional to the gradient along the intensity of the beam. In other words, the gradient force described here tends to attract the particle to the region of highest intensity.

Conclusion :

In order to levitate the particle in air, the downward force of gravity must be countered by the forces stemming from photon momentum transfer. Typically photon radiation pressure of a focused laser beam of enough intensity counters the downward force of gravity while also preventing lateral (side to side) and vertical instabilities to allow for a stable optical trap capable of holding small particles in suspension. Micrometer sized (from several to 50 micrometers in diameter) transparent dielectric spheres such as fused silica spheres, oil or water droplets, are used into morphology-dependent resonances in a spherical optical cavity have been studied by several research groups.

Recommendations :

A cell trapped between the two lasers is trapped at the focal point, but also experiences a gradient of forces from the refracted beams that cause a stretch to its entire volume. This technique functions as long the refractive index of the cell is higher than the surrounding fluid environment. The stretching force that can be generated by the gradients is significantly larger than for two beads pulling with optical tweezers. Also the use of divergent beams produces less risk of radiation damage to the biomolecule or cell.

Acknowledgement :

I would like to express my very great appreciation to Dr Shivaramakrishnan (my professor; you put yours) for his valuable and constructive suggestions during the planning and development of this project work. His willingness to give his time so generously has been very much appreciated.

References :

1. A. Ashkin: Acceleration and trapping of particles by radiation pressure, Phys. Rev. Lett. 24:156-159 (1970)  
2. A. Ashkin, J. M. Dziedzic, J. E. Bjorkholm, S. Chu: Observation of a single-beam gradient force optical trap for dielectric particles, Opt. Lett. 11:288-290 (1986)
3. S. C. Kuo, M. P. Sheetz: Force of single kinesin molecules measured with optical tweezers, Science 260:232-234 (1993)  
4. H.C. v.d. Hulst (Ed.): Light Scattering by Small Particles, Dover, New York (1981)
5. G. Gouesbet, B. Maheu, G. Grehan: Light scattering from a sphere arbitrarily located in a gaussian beam, using a Bromwich formulation, J. Opt. Soc. Am. 5:1427-1443 (1988)