A Study of Trapping Efficiency in Optical Tweezers as a
Function of Beam Profile
Yiyi Deng, Ward Melville High School, East Setauket, NY; Harold Metcalf and John Noé, Laser Teaching Center, Department of Physics and Astronomy, Stony Brook University.
Optical tweezers are an important application of James Clerk Maxwell's 1873 abstraction of radiation pressure, or the ability of light to exert a force. More than a century was to pass before Arthur Ashkin of Bell Laboratories became the first to exploit the theory of radiation pressure by demonstrating optical confinement of transparent latex spheres suspended in aqueous media. Optical tweezers are capable of non-invasive trapping and manipulation of a variety of dielectric nanoparticles and have many interesting applications, especially in biomedical fields. These include chromosome dissection, kinetic studies of DNA and other nucleic acids, DNA injection, controlled cell fusion, microsurgery and manipulation of cells in vivo, in vitro fertilization and finally force measurements of kinesin, organelles, and other sub cellular structures associated with cellular transport and adhesion.
Tweezing theory depends on the ratio of the diameter of the sphere being trapped to the wavelength of the laser light. The ratio of the yeast cell diameter to the wavelength is approximately 5; consequently, the principles of ray optics are used to describe trapping. In this region (known as Mie), the effects of diffraction are neglected and trapping forces are calculated considering the momentum impulse of light due to the reflection and refraction of rays at the surface of the sphere. Since the force on a dielectric object is given by the change in momentum of light induced due to refraction of the light by the object, the total force on the object is the difference between the momentum flux entering the object and that leaving the object. The object is pushed by the reflection of light from its surface while radiation forces due to refraction can be used to pull a transparent object.
In this study, a compact optical tweezers setup has been constructed on a 50x90 cm optical breadboard; the setup consists of a Sharp LT024 780 nm (near-infrared) diode laser, cylindrical and spherical lenses, various first-surface mirrors, and a commercial-quality 1000x oil-immersion microscope. Safety precautions have been taken into consideration in the design of the setup. There are many practical obstacles (mis-alignment of optical elements, laser beam distortions, etc) to achieving the theoretically predicted performance. Optimizing the trap efficiency is especially crucial when working with a relatively low power laser beam. Our setup uses a 20 mW laser (which is not much stronger than a laser pointer), while other research tweezers use lasers 10 - 100 times more powerful. For an optical trap to be stable, the beam must be symmetric about the direction of propagation; this is achieved by careful positioning of the telescoping lens systems and adjustment of the mirrors that lead to the microscope so the beam passes directly through the middle of each lens. Mounting the components as close as possible to the surface of the rigid optical breadboard minimizes changes in alignment due to vibration.
In a past study in this laboratory, modifying the laser beam profile has been shown to increase trapping efficiency, in spite of some loss of beam intensity. I hope to formulate a mathematical model for the dependence of trapping efficiency on beam intensity distribution, and to test this model with appropriate experiments; the light can be redistributed by simply blocking out portions of the beam, or by using an aspheric lens system or a diffractive element. Difficulties already encountered stem from the lack of a mature theoretical explanation of trapping in the complex-Mie region as well as the absence of a universal and effective method for quantifying trapping power.
This research was supported by the Simons Foundation and NSF Grant PHY 00-98044.
An Experimental Evaluation of a Prototype Hydrogenated Amorphous
Yiyi Deng, Ward Melville High School, East Setauket, NY; John Noé and Harold Metcalf, Laser Teaching Center, Dept. of Physics and Astronomy; Charles M. Fortmann, Dept. of Applied Math and Statistics, Stony Brook University.
Guided-Wave Optics involves the transmission of light through dielectric conduits and was originally developed to provide long-distance light transmission without the use of relay lenses. The principle of optical confinement relies on the properties of a medium of one refractive index (which could be in the form of a slab, strip or cylinder) embedded in another medium of lower refractive index; the optical trapping effect results from light rays that are confined by multiple total internal reflections. These light conduits transport light from one location to another with minimal intensity losses.
Fiber optics is the epitome of guided-wave optics at present, but future applications in integrated optical circuitry may prove even more significant in coming decades. Integrated optics is the technology of uniting various optical devices and components for the generation, focusing, splitting, combining, isolation, polarization, coupling, switching, modulation and the detection of light, all on a single substrate. Optical wave guides provide the connections between these components. Such components are optical versions of electronic integrated circuits. Integrated optics has the potential to miniaturize optics, analogous to how integrated circuits have miniaturized electronics.
In 2001, Fortmann et al. demonstrated that the refractive index of amorphous silicon can be dramatically altered upon infusion with hydrogen. The theoretical operations have been performed and a prototype device has been constructed. The prototype has a waveguide channel approximately 5 microns high, 30 microns wide, and 20 mm long. Our immediate goal is to demonstrate that this protototype hydrogen-infused amorphous silicon wave-guide can transmit electromagnetic radiation efficiently. This will be done by focussing laser light from a 1550 nm fiber-coupled laser into the channel at one end and detecting emerging light on the other side. The particular choice of 1550 nm is largely due this wavelength's reputation as a "communications wavelength," facilitating the application of the results in current optical integration technology. The major challenges of the experiment are properly shaping the laser beam at the fiber/wave-guide interface and correctly aligning the wave-guide in the x, y and z planes. At present, we are in the process of selecting suitable laser and motion translation components for purchase.
This research was supported by the Simons Foundation.
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