xvi PREFACE solution.I regularly assign such numerical problems in my own course on ultrafast optics at Purdue University.Although in my experience such problems require substantial effort on the part of the student,they result in a much better understanding of the phenomena involved,not to mention improved skill in applying numerical tools such as the fast Fourier transform.For homework on pulse measurement I have frequently synthesized FROG or other data on a computer;I then distribute the data file to the class with the assignment to process the data to extract the pulse shape.(I have not included such problems in the current book,as I deemed it more expedient to let instructors generate their own pulses and corresponding data files.)The numerical problems included in the book may be used as is or may simply serve to inspire instructors to invent their own numerically oriented problems. Authoring this book has been a project of nearly ten years.I began formal writing while on sabbatical during the 1999-2000 academic year at the Max Born Institute (MBI)for Nonlinear Optics and Ultrashort Pulse Spectroscopy in Berlin,Germany.Work continued for many years,but in a fragmented way,at my home institution.I made substantial progress toward completion during a second sabbatical during the 2006-2007 academic year in Boulder,Colorado,where Isplit my time at the National Institute of Standards of Technology (NIST)and at JILA,a joint enterprise of NIST and the University of Colorado.I owe great thanks to my sabbatical hosts,Prof.Thomas Elsaesser of the MBI,Dr.Leo Hollberg of NIST,and Prof.Steve Cundiff of JILA,for making these stays possible.I would also like to thank the MBI and the Alexander von Humboldt Foundation for assistance with funding during my stay in Berlin and NIST and JILA for assistance with funding during my stay in Boulder. I would like to thank many persons who generously provided input and assistance in various aspects of this project.Giullo Cerullo,Steve Cundiff,Alex Gaeta,and Franz Kaertner provided helpful comments and clarification on various technical topics(in some cases,on multiple topics).Virginia Lorenz made available a copy of her University of Colorado Ph.D.thesis,which provided a very helpful overview of dephasing.At Purdue University,DeeDee Dexter provided invaluable logistical and secretarial assistance through- out the course of this project.Dan Leaird was always willing to lend an ear when I wanted to voice ideas about the book project;Dan also deserves great thanks for his unflagging attention to our ultrafast optics and fiber communications research laboratory,even when I sometimes became distracted by the burdens of authorship.Many students deserve credit for identifying errors in preliminary versions of the manuscript,which were used over sev- eral iterations of my graduate course.Prof.Dongsun Seo,a sabbatical visitor from Korea, also pointed out several items in need of correction.A number of graduate students kindly agreed to carry out numerical work,generating data that resulted in a number of figures. These students include Jung-Ho Chung,Ehsan Hamidi,Zhi Jiang,Houxun Miao,Bhaskaran Muralidharan,Ninad Pimparkar,Haifeng Wang,Mark Webster,and Shang-Da Yang.V.R Supradeepa checked several equations on my behalf.Zhi Jiang was especially helpful in proofing the typeset manuscript. This book includes well over 200 figures,many of which were composed especially for this project.Although many others were taken from the literature,almost all of these were modified or redrawn to ensure readability and to achieve consistency of appearance and notation.I am tremendously grateful to Bill Drake,Jr.,for fulfilling this responsibility with great skill from the inception of this project until it neared completion.Tragically,Bill succumbed to cancer at an early age.He continued to contribute to this book even as he struggled against the disease that ultimately killed him.Michael Black took over technicalxvi PREFACE solution. I regularly assign such numerical problems in my own course on ultrafast optics at Purdue University. Although in my experience such problems require substantial effort on the part of the student, they result in a much better understanding of the phenomena involved, not to mention improved skill in applying numerical tools such as the fast Fourier transform. For homework on pulse measurement I have frequently synthesized FROG or other data on a computer; I then distribute the data file to the class with the assignment to process the data to extract the pulse shape. (I have not included such problems in the current book, as I deemed it more expedient to let instructors generate their own pulses and corresponding data files.) The numerical problems included in the book may be used as is or may simply serve to inspire instructors to invent their own numerically oriented problems. Authoring this book has been a project of nearly ten years. I began formal writing while on sabbatical during the 1999–2000 academic year at the Max Born Institute (MBI) for Nonlinear Optics and Ultrashort Pulse Spectroscopy in Berlin, Germany. Work continued for many years, but in a fragmented way, at my home institution. I made substantial progress toward completion during a second sabbatical during the 2006–2007 academic year in Boulder, Colorado, where I split my time at the National Institute of Standards of Technology (NIST) and at JILA, a joint enterprise of NIST and the University of Colorado. I owe great thanks to my sabbatical hosts, Prof. Thomas Elsaesser of the MBI, Dr. Leo Hollberg of NIST, and Prof. Steve Cundiff of JILA, for making these stays possible. I would also like to thank the MBI and the Alexander von Humboldt Foundation for assistance with funding during my stay in Berlin and NIST and JILA for assistance with funding during my stay in Boulder. I would like to thank many persons who generously provided input and assistance in various aspects of this project. Giullo Cerullo, Steve Cundiff, Alex Gaeta, and Franz Kaertner provided helpful comments and clarification on various technical topics (in some cases, on multiple topics). Virginia Lorenz made available a copy of her University of Colorado Ph.D. thesis, which provided a very helpful overview of dephasing. At Purdue University, Dee Dee Dexter provided invaluable logistical and secretarial assistance through￾out the course of this project. Dan Leaird was always willing to lend an ear when I wanted to voice ideas about the book project; Dan also deserves great thanks for his unflagging attention to our ultrafast optics and fiber communications research laboratory, even when I sometimes became distracted by the burdens of authorship. Many students deserve credit for identifying errors in preliminary versions of the manuscript, which were used over sev￾eral iterations of my graduate course. Prof. Dongsun Seo, a sabbatical visitor from Korea, also pointed out several items in need of correction. A number of graduate students kindly agreed to carry out numerical work, generating data that resulted in a number of figures. These students include Jung-Ho Chung, Ehsan Hamidi, Zhi Jiang, Houxun Miao, Bhaskaran Muralidharan, Ninad Pimparkar, Haifeng Wang, Mark Webster, and Shang-Da Yang. V. R. Supradeepa checked several equations on my behalf. Zhi Jiang was especially helpful in proofing the typeset manuscript. This book includes well over 200 figures, many of which were composed especially for this project. Although many others were taken from the literature, almost all of these were modified or redrawn to ensure readability and to achieve consistency of appearance and notation. I am tremendously grateful to Bill Drake, Jr., for fulfilling this responsibility with great skill from the inception of this project until it neared completion. Tragically, Bill succumbed to cancer at an early age. He continued to contribute to this book even as he struggled against the disease that ultimately killed him. Michael Black took over technical