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Chapter 1 Theoretical Treatm SIMULTANEOUS TWO-PHOTON ABSORPTION OF TETRAPYRROLIC MOLECULES: FROM FEMTOSECOND COHERENCE EXPERIMENTS TO PHOTODYNAMIC THERAPY by Aliaksandr Karotki A dissertation submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy in Physics MONTANA STATE UNIVERSITY Bozeman, Montana December 2003 COPYRIGHT by Aliaksandr Karotki 2003 All Rights Reserved ii APPROVAL of a dissertation submitted by Aliaksandr Karotki This dissertation has been read by each member of the dissertation committee and has been found to be satisfactory regarding content, English usage, format, citations, bibliographic style, and consistency, and is ready for submission to the College of Graduate Studies. Aleksander Rebane Approved for the Department of Physics William A. Hiscock Approved for the College of Graduate Studies Bruce R. McLeod iii STATEMENT OF PERMISSION TO USE In presenting this dissertation in partial fulfillment of the requirements for a doctoral degree at Montana State University, I agree that the Library shall make it available to borrowers under rules of the Library. I further agree that copying of this dissertation is allowable only for scholarly purposes, consistent with “fair use” as described in the U.S. Copyright Law. Requests for extensive copying or reproduction of this dissertation should be referred to Bell & Howell Information and Learning, 300 North Zeeb Road, Ann Arbor, Michigan 48106, to whom I have granted “the exclusive right to reproduce and distribute my dissertation in and from microform along with the non-exclusive right to reproduce and distribute my abstract in any format in whole or in part.” iv ACKNOWLEDGEMENTS This thesis is the result of four years of work whereby I have been accompanied and supported by many people. It is a pleasant aspect that I have now the opportunity to express my gratitude to all of them. First, let me thank my advisor, Prof. Aleksander Rebane, for giving me an opportunity to be a part of this challenging research project. His advices and constant help kept me moving forward. Aleks’s overall enthusiasm and integral view on research and his mission for providing ‘only high-quality work and not less’, have made a deep impression on me. I owe him lots of gratitude for having shown me this way of research. I would like to thank Dr. Mikhail Drobizhev, the Research Assistant Professor in our group, who kept an eye on the progress of my work, participated in many of the experiments described here, and always was available when I needed an advice. Mikhail’s ability to come up with theoretical explanation for about anything that we encountered in our experiments proved to be crucially important. Without his encouragement, instruction, and leadership this thesis would not exist. My thanks are also to Dr. Mikalai Kruk. He was my scientific adviser back in Belarus when I was an undergraduate student and as such he started my career in science. During his visits to Dr. A. Rebane lab, Mikalai participated in many experiments described in the thesis. I also would like to thank many people from different chemistry departments around the world, who contributed to this work by synthesizing molecules with unique v properties that we investigated. My special thanks are to Prof. Charles W. Spangler, Dr. Fanquing Meng, and Dr. Erik Nickel from Department of Chemistry and Biochemistry, Montana State University, Bozeman, USA, Prof. Harry L. Anderson and Dr. Peter N. Taylor from Chemistry Department, University of Oxford, Oxford UK, Dr. Nugzar Mamardashvili from Institute of Solution Chemistry, Ivanovo, Russia. My thanks are also to Prof. Rufus Cone for his kind loan of IR-detector whenever we needed it. Without this detector, the Chapter 5 of this thesis would never be written. Finally, the person that I am grateful the most is my wife Yuliya Dzenis. She participated in many experiments described here and provided support for simulations and quantum-chemical calculations with Hyperchem. But most of all I am grateful to her for her love and patience that allowed me to finish this work. vi TABLE OF CONTENTS 1. INTRODUCTION ..........................................................................................................1 Introduction to Research Topic.......................................................................................1 Overview of Thesis.........................................................................................................6 2. TWO-PHOTON ABSORPTION: THE MAIN CONCEPTS AND THEORETICAL CONSIDERATIONS .........................................................................8 The Main Concepts of TPA ............................................................................................8 Theoretical Treatment of TPA......................................................................................11 Three-Level Model .......................................................................................................17 Three-Level Model for a Centrosymmetrical Molecule .......................................... 18 Three-Level Model for a Non-Centrosymmetrical Molecule.................................. 21 3. TPA PROPERTIES OF TETRAPYRROLIC COMPOUNDS AND METHODS OF ENHANCEMENT OF TWO-PHOTON CROSS SECTION ............25 Porphyrins and their Derivatives ..................................................................................27 Previous Work on Nonlinear Absorption of Tetrapyrrolic Molecules .........................34 Experimental.................................................................................................................37 TPA Properties of Tetrapyrrolic Molecules in the Transitions Spectral Region Corresponding to the Q-bands..........................................................................54 Resonance Enhancement of TPA in the Spectral Region Corresponding to One-Photon Soret Transition ....................................................................................62 Enhancement of TPA due to g-g transitions.................................................................76 Other Approaches to the TPA Enhancement................................................................82 New Method for Measuring Absolute TPA Cross Section...........................................89 4. TPA-INDUCED FREQUECY DOMAIN COHERENCE GRATINGS......................97 Theoretical Description of Coherence Grating Excited by TPA in Inhomogeneously Broadened Medium.......................................................................101 Experimental...............................................................................................................105 Two-Photon-Excited Coherence Gratings Detected by SHB .....................................109 Two-Photon Excited Coherence Gratings Detected by Fluorescence ........................116 Temperature Dependence of Spectral Gratings ..........................................................120 Theoretical Model.................................................................................................. 120 Simulation and Discussion..................................................................................... 126 vii TABLE OF CONTENTS - CONTINUED 5. PHOTOSENSITIZATION OF SINGLET MOLECULAR OXYGEN BY MEANS OF TWO-PHOTON EXCITATION AND ITS APPLICATION FOR PDT.........................................................................................135 What is PDT................................................................................................................137 Experimental...............................................................................................................142 Two-Photon Excitation of Some Currently Used Photosensitizers ............................148 New Porphyrin-Based Compounds for PDT with Greatly Enhanced TPA Cross Sections ....................................................................................................155 6. SUMMARY AND CONCLUSION ...........................................................................171 TPA Properties of Tetrapyrrolic Compounds and Methods of Enhancement of Two-Photon Cross Section (Chapter 3)...........................................171 TPA-Induced Frequency Domain Coherence Gratings (Chapter 4)...........................174 Photosensitization of Singlet Molecular Oxygen by Means of Two-Photon Excitation and Its Application for PDT (Chapter 5)..............................176 REFERENCES CITED....................................................................................................178 APPENDICES .................................................................................................................200 APPENDIX A: PARITY SELECTION RULES FOR THE TWO-PHOTON TRANSITIONS.............................................................................201 APPENDIX B: EVALUATION OF THE ABSOLUTE TPA CROSS SECTION..................................................................................................................204 APPENDIX C: RELATIONS BETWEEN TRANSITION DIPOLE MOMENT, OSCILLATOR STRENGTH, LINE SHAPE FUNCTION, AND MOLAR EXTINCTION COEFFICIENT.......................................................209 APPENDIX D: DERIVATION OF THE EXPRESSION DESRIBING FREQUENCY GRATING IN THE FLUORESCENCE SPECTRUM CREATED WITH TWO-PHOTON EXCITATION................................................214 viii LIST OF TABLES Table Page 3.1 Comparison of the two main experimental techniques used for two- photon cross section measurements, fluorescence-based and Z-scan. The
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