Localized Dynamic Lensing with Extended Depth of Field
Our lab is in the process of designing a new class of dynamic AO (acousto-optic) lenses that utilize a periodic refractive index to realize ultra-high-speed variable focusing. Our scheme sets itself apart from the leading ultra-fast acousto-optic method with its ability to handle continuous wave sources, avoiding the need for synchronizing the acoustic signal to a laser source. The principle underlying its function is the acousto-optic analog of the Kapitza-Dirac effect, where parametric interaction between an ultrasonic field and a Gaussian beam can be exploited to stably confine light within the central acoustic lobe. We attain variable focusing by amplitude modulation on the RF signal to the transducer, enabling incredibly fast switching speeds limited only by the bandwidth of the transducer.
To experimentally realize this effect, light must be precisely guided into this central lobe to propagate over a fixed number of acoustic wavelengths. Since this alignment is challenging in free space, I am currently working on coupling the laser into an optical fiber and designing a housing which appropriately aligns the fiber with the transducer (up to machining tolerances). The work has required me to learn more advanced theoretical techniques such as Gaussian beam propagation, where I use ray transfer matrices to put together an optical system which tailors a laser beam’s characteristics to our requirements. I have extended these analytical tools into Mathematica and Matlab codes which predict the system parameters needed to match the field pattern to the fundamental mode of a GRIN-rod.
The continuous waist output of the acousto-optic interaction gives birth to applications such as controllable in-depth imaging, and incisions. For instance, the implications could be found in performing minimally invasive surgery. When shadowing a doctor during a summer of high school, I witnessed the process during which the doctors used a camera on a probe to inspect a patient's lumbar area to help remove a bulge on his disc. The patient suffered pain as the doctor wrenched the probe into his body to locate the bulge. With the acoustic lens, it is possible that this surgery could be conducted without having to squish the probe in the patient’s body and cause unnecessary invasions by enplying in-depth imaging of the acoustic lens.
Citation: Mercedeh K., Localized Dynamic Lensing with Extended Depth of Field via Longitudinal Light-Sound
Vision
Working on this research enabled me to experiment with various mathematical calculations such as Maxwell’s equation and waist equations. Fighting my way in the forest of the unknown honed my perception of the essential concepts of the project and sculptured a spirit of persistence and faithfulness. While I am fascinated by the innovative approach of this research, I am more intrigued by the mathematical side of simulating the pathway for the beam such that the foci of the outputs are maximized. In the future, I aspire to engage in research that involves highly applied mathematics. I look forward to making connections with various disciplines that may inspire interesting and useful mathematics applications where innovative mathematical reasoning whether it be probability or differential equations may lead to new insights.
In out Laboratory, we built a cart that measured the temperature changes within a tank where acoustics interact with optic waves. Applying the concepts in my recent physics lecture to leverage the properties of electric and magnetic forces, I manipulated the amplitude and direction of current based on the thermodynamics of the environment. This adjustment on the current induces a magnetic force that propels the cart to move in the direction of heat, allowing for temperature distribution measurements based on acoustic and optic wave intensities.
