Young Scholars Alumni

Abstract:
James Clerk Maxwell revolutionized the field of optics when he asserted his theory on radiation pressure in 1871. Nearly a century later, Arthur Ashkin expanded Maxwell's theory with his paper "Acceleration and trapping of particles by radiation pressure" (1970). In this paper, Ashkin laid the groundwork that showed how radiation pressure can be exploited with lasers to produce forces with which microscopic particles can be manipulated. Ashkin overcame the inherent hindrance of the thermal forces that overpower optical forces by using powerful lasers and non-absorbing, transparent microparticles. His initial setup included two-beams pointed against each other. This allows a particle to be placed symmetrically between the two beams where the optical forces can cancel and suspend the particle in equilibrium. Another configuration, called a hybrid setup, allows for one beam to be placed under the particle, so that the optical force counteracts the gravitational force, leaving the particle stationary. But the real breakthrough came in 1986, when Ashkin discovered that a single beam can be focused in a way that allows for the particle to be held immobile without the assistance of other, outside forces—Ashkin called this setup the "optical tweezers." From this finding a new field of optics was created in which research proliferates and two Nobel Prizes have since been awarded.

To understand optical tweezers we must first understand the dynamics of radiation pressure. We know that when light hits a dielectric particle, some light is reflected and the rest is refracted. We also know that light waves carry momentum, so when the light is refracted its velocity changes and therefore its momentum also changes. This change in momentum imparts a force, and this is the force that can be used to move the particle. All of the light rays considered collectively superimpose to produce one large force that can be resolved into two components, the gradient force, directed towards the area of greatest light intensity, i.e. the beam's focus; and the scattering force, which points in the direction of the beam propagation. The optical tweezers setup makes use of these forces in an interesting way. A microscopic objective is used to focus the beam so tightly that the gradient force can overcome the scattering force and the thermal forces, and shift the particle to region of highest intensity-the focus-where it is held in equilibrium. Optical tweezers are versatile and can be incorporated in all fields of science. Current active research areas include drug delivery via cell poration, antibody and antigen binding, and optically controlled collisions.

I investigated the effects of optical tweezers on particles during my internship under Prof. Jalali at the University of California, Los Angeles, made possible by the Center for Integrated Access Networks (CIAN). Much of my time in the Photonics Lab was spent learning the mathematics and concepts that govern electromagnetic waves and Maxwell’s equations. These included learning vector algebra, gradients, the concepts of divergence and curl including the fundamental theorems by which these can be applied, the deeper mechanics of electric and magnetic fields, Gaussian functions, etc. I gave weekly presentations to my mentor, Peter DeVore, which showed all that I learned and its potential uses, and I completed assignments to demonstrate my understanding of these concepts, e.g. proving the superposition principle with Fourier Transforms. Next I learned to code in MATLAB. I began by writing codes to implement concepts that I had already learned. These codes included plotting Gaussian functions; using Taylor Series approximations to plot complicated functions and calculate their error; and using the Euler and Leapfrog algorithms to estimate the solutions of differential equations. I then wrote and ran simulations that were more pertinent to optical tweezers, including a simulation that demonstrated the deflection of silica nanoparticles using optical tweezers. In the process of learning and coding I was not only able to carry out the given tasks, but I also began to build an intuition for the physics behind these tasks. The knowledge I gained from the experience will assist me for years to come when I pursue a physics degree in college.

Abstract:
This past summer, I had the outstanding opportunity of interning at Dr. Jalali's photonics lab at UCLA. I worked on a project called Time Stretch Analog to Digital Conversion (TS-ADC). This project's goal is to sample high bandwidth analog signals in real time with less noise and less power consumption. The current method of high bandwidth analog to digital conversion (ADC), referred to as time interleaving, requires that the signal be split up into parts, each part sampled separately by different low speed ADCs, and then be put back together once interpreted. The time interleaving method, however, is inaccurate. The different sampled segments do not perfectly align after being recombined, resulting in jitter and lower signal to noise ratio (SNR). Time Stretch solves this problem by splitting up the signal into different parts and then slowing down each part, reducing the analog bandwidth, so that each part can be sampled by low speed ADCs in real time. By using Time Stretch, there is no need to precisely realign the outputs of separate ADCs, resulting in less jitter and a more accurate interpretation of the signal.

The aspect of Time Stretch upon which I focused was creating a method of calculating the Bit Error Rate (BER) of high bit rate communication signals sampled using the Time Stretch Enhanced Recording (TiSER) oscilloscope, a single channel version of the TS-ADC. Given that signals are interpreted in binary, the BER is a measure of the number of incorrect readings of zeros and ones divided by the total number of zeros and ones. Ideally, the BER of a signal is negligible. I used Matlab to generate eye diagrams of signals from the TiSER data. In order to approximate the noise in the eye diagram, I fit Gaussian functions to the top and bottom halves of the eye. The standard deviations of these Gaussians served as an estimate of the noise in the signal. Once the standard deviations and means of the Gaussians were determined, I integrated the portion of the upper Gaussian lying below a certain threshold level, and the portion of the lower Gaussian lying above the threshold level, and added the two in order to obtain the probability of an error occurring. The ideal threshold level was also determined and the BER corresponding to that threshold level calculated. Furthermore, I calculated the BER at different times along the eye. The time at which the BER was a minimum was used as an estimate for the center of the eye. The code I created in Matlab provides for an automated method for determining the BER of a signal, and along with TiSER's real time capabilities, allows for incredibly fast and accurate BER analysis of high bit rate signals.