Chaotic Dynamics of a Laser with Feedback

Title of dissertation: CHAOTIC DYNAMICS OF A LASER WITH FEEDBACK Ryan Glen McAllister, Doctor of Philosophy, 2003 Dissertation directed by: Professor Rajarshi Roy Department of Physics A diode-pumped solid-state laser is constructed. The complex dynamics resulting from electronic feedback of the laser intensity are explored and characterized. The laser is further perturbed by periodic, quasiperiodic, and chaotic drives. Distinct stable and chaotic regimes can be elicited from the laser by tuning the bias of the feedback loop. An additional branch of the feedback loop, containing a derivative filter, provides access to new kinds of dynamics, including a more gradual transition to chaos. The whole feedback network together allows the laser dynamics to be selected from among a wide range of chaotic waveforms distinguished by statistical or spectral information. In other words, this laser system can be used as a tunable generator of chaotic functions. The laser with feedback is perturbed by a signal composed of one or two sinusoids. The phase of the chaotic intensity signal is constructed using the complex analytic signal. With one-frequency driving, the laser dynamics show phase entrainment for sufficient driving amplitude. Competition between two distinct driving frequencies to phase synchronize the intensity dynamics of a chaotic laser is observed in the case of two-frequency driving. Competing frequencies alternately show phaselocking and phase-slipping. Competition is quantified by calculating the portion of time the laser phase-locks to each of the driving frequencies and their average. The electronic feedback signal driving the chaotic dynamics of a laser is recorded. Feedback is removed and the recorded signal is replayed to the laser. Instead of repeating the original dynamics, the laser displays generalized synchronization to its previous waveform. Generalized synchronization error is minimized for slightly mismatched laser parameters. In addition, the generalized synchronization includes phase synchronization between drive and response with synchronized phase slips. A physical mechanism for generalized synchronization relying on hidden variables of the laser is proposed. A model including this mechanism is investigated and shows good agreement with the experiment. CHAOTIC DYNAMICS OF A LASER WITH FEEDBACK by Ryan Glen McAllister Dissertation submitted to the Faculty of the Graduate School of the University of Maryland, College Park in partial fulfillment of the requirements for the degree of Doctor of Philosophy 2003 Advisory Committee: Professor Rajarshi Roy, Chair/Advisor Professor Brian Hunt Professor Daniel P. Lathrop Professor Edward Ott Dr. Ira B. Schwartz c © Copyright by Ryan Glen McAllister 2003 Perhaps the best thing you can give a person is a pretty good start. I would like to thank Jill, Richard, Jocelyn, and RJ McAllister, and William W. and Betty Sunderlin for that start in terms of family. I owe much gentleness in the early years of my life to my extended family and family friends including Mr. and Mrs. Crawford, Jerry Manning, Judy and Dwayne Singley, Uncle Bill and Aunt Sybill, Aunt Fran and Uncle Chuck, Linda, Leslie and Mema, Janus and Mr. and Mrs. Hart, and Julie Cobern. I owe many thanks also to the family I do not yet know. Lynn Leaf, Pat Distephano, Mr. Hale, Mrs. Prince, Mrs. Schroder, Dr. Hunt, and others were very kind in elementary school. Smitha Henyumaiah, thank you for showing me understanding and compassion. Mrs. Hicks, Mrs. Krupp, Dr. Hartman, Mrs. Taylor, Mr. Czapsky, and Mrs. Gise, thanks for encouraging me and taking concern with me when I needed it. Virginia Curtis, Mrs. Jewett, Mr. Hutchinson, Mr. Craig, Mrs. Ames, Mme Simone, Mme Micka were great teachers, and I appreciate their tutelage while I was in high school. Vadim Bindler, Stephan, Kristin Botts, Mrs. Botts, Coach Singleton, and Mrs. Taylor, thank you for making being a gymnast and runner possible and fun. William Elliott (the 3rd), Michael Vatalaro, Daniel Ryder, Jessie Strauss, Ethan Fingerman, Amanda Beckenstein (now Mbuvi), Kelly Naylor, Mike Bramer, Angela Menegay, Peter McCabe and Maryland Search and Rescue Group 616, Anne Ryder, Maya Thompson, Soo-Ann Roberts, Diane, Erin Slonaker and David Rosenberg were friends in high school and always. I would like to thank Juan Lin, Satinder Sidhu, Eugene Hamilton, Louise Amick, Albert Briggs, Angela Dover, Bob Anderson, Kevin Brien, Eugenia Porto, Christine Pabon, Garry Clarke, James Locker, Frank Creegan, Robert Mooney, Don Munson, Michael Kerchner, George Spilich, Gail Tubbs, Cathy Waye, Gene Narcum, Jack Hamilton, Linda Cades, Bob Day, Colin Dickson, John Toll, Christina Turner, Jason Samus, Corey Stottlemeyer, David Gillis, Jessa DeMars, Billie Rinaldi, Kelly Beckwith, Ellyn Baines, Beth Moser, Nicole Guimond, Matt Korey, Jeff Frank, Eva Kaplan-Leiserson, Courtney Clulow, Sita Nataraj, Elitsa Hadgieva, and Joellen