PREFACE xvii illustration responsibilities during the final period of this project;he also deserves much gratitude. Finally,I would like to thank my parents,Jason and Geraldine Weiner,for fostering in me a love of learning;my graduate advisors,Profs.Hermann Haus and Erich Ippen,for attracting me to the field of ultrafast optics;and my wife,Brenda,and children,Roberta, Steven,and Gabriela,for their love and patience. ANDREW M.WEINER West Lafayette,Indiana September 2008
PREFACE xvii illustration responsibilities during the final period of this project; he also deserves much gratitude. Finally, I would like to thank my parents, Jason and Geraldine Weiner, for fostering in me a love of learning; my graduate advisors, Profs. Hermann Haus and Erich Ippen, for attracting me to the field of ultrafast optics; and my wife, Brenda, and children, Roberta, Steven, and Gabriela, for their love and patience. Andrew M. Weiner West Lafayette, Indiana September 2008
INTRODUCTION AND REVIEW 1.1 INTRODUCTION TO ULTRASHORT LASER PULSES This book is about ultrafast laser pulses:what they are,linear and nonlinear optical effects which they experience,methods by which they are generated and measured,and how they can be used for measurement of ultrafast physical processes.Let us begin with a definition of the relevant time units. 1 nanosecond (ns)=10-9s =0.000000001s 1 picosecond(ps)=10-l2s=0.000000000001s 1 femtosecond(fs)=10-l5s=0.000000000000001s 1 attosecond =10-18s=0.000000000000000001s To put these very short time units in perspective,it is useful to consider their spatial equiva- lent.If we could take a snapshot of a 1-s light pulse,this pulse would stretch over a distance of 186,000 miles(or 300,000 km),equal to the speed of light multiplied by 1s.This is roughly three-fourths of the distance from the Earth to the moon,a distance we will consider very slow!Now skipping over milliseconds and microseconds,we arrive at nanoseconds.One nanosecond has a spatial extent of 30 cm(ca.I ft).Although still rather slow by the standards of ultrafast optics,the nanosecond is the approximate time scale for high-speed electronic chips and computers.The word ultrafast is usually applied to the picosecond time scale and below.A picosecond has an extent of 0.3 mm,roughly the thickness of a business card. Given that typical garden-variety laser beams have beam diameters on the order of a few millimeters,we should perhaps envision pulses a picosecond and shorter not as pencils of light but as pancakes of light!In the visible and near-infrared spectral regions,pulses as Ultrafast Optics,By Andrew M.Weiner Copyright 2009 John Wiley Sons,Inc 1
1 INTRODUCTION AND REVIEW 1.1 INTRODUCTION TO ULTRASHORT LASER PULSES This book is about ultrafast laser pulses: what they are, linear and nonlinear optical effects which they experience, methods by which they are generated and measured, and how they can be used for measurement of ultrafast physical processes. Let us begin with a definition of the relevant time units. 1 nanosecond (ns) = 10−9 s = 0.000000001s 1 picosecond (ps) = 10−12 s = 0.000000000001s 1 femtosecond (fs) = 10−15 s = 0.000000000000001s 1 attosecond = 10−18 s = 0.000000000000000001s To put these very short time units in perspective, it is useful to consider their spatial equivalent. If we could take a snapshot of a 1-s light pulse, this pulse would stretch over a distance of 186,000 miles (or 300,000 km), equal to the speed of light multiplied by 1s. This is roughly three-fourths of the distance from the Earth to the moon, a distance we will consider very slow! Now skipping over milliseconds and microseconds, we arrive at nanoseconds. One nanosecond has a spatial extent of 30 cm (ca. 1 ft). Although still rather slow by the standards of ultrafast optics, the nanosecond is the approximate time scale for high-speed electronic chips and computers. The word ultrafast is usually applied to the picosecond time scale and below. A picosecond has an extent of 0.3 mm, roughly the thickness of a business card. Given that typical garden-variety laser beams have beam diameters on the order of a few millimeters, we should perhaps envision pulses a picosecond and shorter not as pencils of light but as pancakes of light! In the visible and near-infrared spectral regions, pulses as Ultrafast Optics, By Andrew M. Weiner Copyright © 2009 John Wiley & Sons, Inc. 1
2 INTRODUCTION AND REVIEW short as a few femtoseconds can now be generated.The spatial extent of even a 10-fs laser pulse is only 3 um,much less than the diameter of a human hair. Pulse durations of a few femtoseconds in the visible are approaching the fundamental pulse-width limitation of roughly one optical cycle(roughly one wavelength in spatial extent).Research into attosecond pulse generation is also under way [1].One key theme in attosecond pulse generation is the use of highly nonlinear optical frequency-conversion methods to produce radiation at much higher frequencies(much shorter wavelengths). corresponding to extreme ultraviolet(XUV)and x-ray spectral regions.At such frequencies the duration of a single optical cycle (and hence the attainable pulse-width limit)is reduced, making attosecond pulses possible. In this book we specifically focus on ultrafast optics in visible and lower-frequency spectral bands and on time scales down to femtoseconds.Within this time scale the motions of bound electrons that mediate important laser-matter interactions may usually be viewed as instantaneous.Conversely,attosecond time scales and XUV and x-ray frequencies bring in entirely new physics in which laser-matter interactions are sensitive to the noninstantaneous dynamics of bound electron motions.Attosecond technology and science are in a stage of rapid evolution and will undoubtedly be the subject of future books. Ultrashort pulses have several related characteristics which make them useful for appli- cations.These include the following: High time resolution.By definition,the pulse duration is in the picosecond or fem- tosecond range (or below).This provides very high time resolution for excitation and measurement of ultrafast physical processes in solid-state,chemical,and biological materials. High spatial resolution.The spatial extent of a short light pulse is given by the pulse duration multiplied by the speed of light.As noted above,for very short pulse durations, the spatial pulse length can be on the order of micrometers.This makes ultrashort pulses useful for some microscopy and imaging applications. High bandwidth.By the uncertainly principle,the product of the pulse-width times the optical bandwidth must be of order unity(or larger).As the pulse duration decreases, the bandwidth increases correspondingly.Pulses of 100 fs have bandwidths on the order of 10 terahertz(THz).and the shortest visible laser pulses contain so much of the visible spectrum that they appear white.This high-bandwidth feature can be important for optical communications as well as other applications. Potential for high intensity.For a given pulse energy,the peak power and peak inten- sity are inversely proportional to the pulse duration.Because the size (hence cost) of high-power lasers usually scales with pulse energy,femtosecond pulse technology can be used to obtain ultrahigh peak intensities at moderate energy levels.Amplified femtosecond pulses have produced peak powers up to the petawatt level(1 petawatt 1015 W)and peak intensities exceeding 1020 W/cm2. The field of ultrafast optics has traditionally been a highly interdisciplinary one,with a wide range of applications areas.To give a flavor for the nature of application areas,we comment below on a few of the research applications Ultrafast Spectroscopy Time-resolved spectroscopy is a very successful and probably the most widespread application of picosecond and femtosecond laser technology.The idea
2 INTRODUCTION AND REVIEW short as a few femtoseconds can now be generated. The spatial extent of even a 10-fs laser pulse is only 3m, much less than the diameter of a human hair. Pulse durations of a few femtoseconds in the visible are approaching the fundamental pulse-width limitation of roughly one optical cycle (roughly one wavelength in spatial extent). Research into attosecond pulse generation is also under way [1]. One key theme in attosecond pulse generation is the use of highly nonlinear optical frequency-conversion methods to produce radiation at much higher frequencies (much shorter wavelengths), corresponding to extreme ultraviolet (XUV) and x-ray spectral regions. At such frequencies the duration of a single optical cycle (and hence the attainable pulse-width limit) is reduced, making attosecond pulses possible. In this book we specifically focus on ultrafast optics in visible and lower-frequency spectral bands and on time scales down to femtoseconds. Within this time scale the motions of bound electrons that mediate important laser–matter interactions may usually be viewed as instantaneous. Conversely, attosecond time scales and XUV and x-ray frequencies bring in entirely new physics in which laser–matter interactions are sensitive to the noninstantaneous dynamics of bound electron motions. Attosecond technology and science are in a stage of rapid evolution and will undoubtedly be the subject of future books. Ultrashort pulses have several related characteristics which make them useful for applications. These include the following: High time resolution. By definition, the pulse duration is in the picosecond or femtosecond range (or below). This provides very high time resolution for excitation and measurement of ultrafast physical processes in solid-state, chemical, and biological materials. High spatial resolution. The spatial extent of a short light pulse is given by the pulse duration multiplied by the speed of light. As noted above, for very short pulse durations, the spatial pulse length can be on the order of micrometers. This makes ultrashort pulses useful for some microscopy and imaging applications. High bandwidth. By the uncertainly principle, the product of the pulse-width times the optical bandwidth must be of order unity (or larger). As the pulse duration decreases, the bandwidth increases correspondingly. Pulses of 100 fs have bandwidths on the order of 10 terahertz (THz), and the shortest visible laser pulses contain so much of the visible spectrum that they appear white. This high-bandwidth feature can be important for optical communications as well as other applications. Potential for high intensity. For a given pulse energy, the peak power and peak intensity are inversely proportional to the pulse duration. Because the size (hence cost) of high-power lasers usually scales with pulse energy, femtosecond pulse technology can be used to obtain ultrahigh peak intensities at moderate energy levels. Amplified femtosecond pulses have produced peak powers up to the petawatt level (1 petawatt = 1015 W) and peak intensities exceeding 1020 W/cm2 . The field of ultrafast optics has traditionally been a highly interdisciplinary one, with a wide range of applications areas. To give a flavor for the nature of application areas, we comment below on a few of the research applications. Ultrafast Spectroscopy Time-resolved spectroscopy is a very successful and probably the most widespread application of picosecond and femtosecond laser technology. The idea
INTRODUCTION TO ULTRASHORT LASER PULSES 2 is that ultrashort laser pulses can be used to make "stop-action"measurements of ultra- fast physical processes,just as high-speed(microsecond)electronic flashes have been used starting several decades ago to make such stop-action photographs of bullets traveling through apples and milk droplets splashing into milk bowls [2].On the femtosecond time scale,macroscopic objects such as bullets and milk droplets are motionless,and therefore ultrafast spectroscopy is best applied to study microscopic processes.Examples include investigations of femtosecond interactions of photoexcited electrons and holes with each other and with lattice vibrations in semiconductor crystals,ultrafast laser-induced melting, photodisassociation and ultrafast solution dynamics of chemical species,and ultrafast in- ternal rearrangements of the large organic molecule bacteriorhodopsin as photons absorbed in the retina initiate the first biochemical steps in the process of vision.The principles of ultrafast spectroscopy are covered in Chapter 9 with examples. Laser-Controlled Chemistry In a research area closely related to ultrafast spectroscopy, researchers are using specially engineered femtosecond laser waveforms to try to influence the course of photoinduced chemical reactions.In addition to observing ultrafast chemical motions as in time-resolved spectroscopy.the added idea here is to control the motions that take place.Since the intrinsic time scale for nuclear motions in chemical systems is tens to hundreds of femtoseconds,femtosecond laser pulses are a natural tool in pursuing the challenging goal of laser-controlled chemistry. Frequency Metrology Ultrashort pulses are usually emitted from lasers in the form of periodic trains,which under certain conditions can exhibit very high timing stability and long-term coherence.The spectrum of such a periodic train is a comb of up to hundreds of thousands of discrete spectral lines,which may be stabilized to permit precision mea- surements of optical frequencies with sub-hertz uncertainties across the optical spectrum. Such stabilized frequency combs are now widely adopted for high-precision frequency metrology and for investigations of precision optical clocks.Related topics are discussed in Section 7.5. High-Speed Electrical Testing Testing is a key issue in the development of high-speed electronic devices and circuits.Electronic test instrumentation based on established tech- nology is usually slower than advanced high-speed research devices.However,since even the very fastest electronic devices only reach into the picosecond range,ultrafast laser tech- nology offers speed to spare.Thus femtosecond optical pulses have been applied to generate subpicosecond electrical pulses and to measure operation of the highest-speed electronic devices.Ultrafast electrical pulse generation and measurement are discussed in Chapter 10. Laser-Plasma Interactions Lasers with intensities of 1013 W/cm2 and above (easily achieved using amplified femtosecond pulses)directed onto solid targets are sufficient to strip electrons from their nuclei,resulting in a laser-generated plasma.On the 100-fs time scale,the resulting free electrons do not have enough time to separate from the ionized nuclei.This provides the opportunity to study solid-density plasmas at temperatures as high as I million degrees. Short-Wavelength Generation High-intensity ultrashort pulses at visible wavelengths can also be used to generate coherent short-wavelength radiation in the vacuum ultraviolet and
INTRODUCTION TO ULTRASHORT LASER PULSES 3 is that ultrashort laser pulses can be used to make “stop-action” measurements of ultrafast physical processes, just as high-speed (microsecond) electronic flashes have been used starting several decades ago to make such stop-action photographs of bullets traveling through apples and milk droplets splashing into milk bowls [2]. On the femtosecond time scale, macroscopic objects such as bullets and milk droplets are motionless, and therefore ultrafast spectroscopy is best applied to study microscopic processes. Examples include investigations of femtosecond interactions of photoexcited electrons and holes with each other and with lattice vibrations in semiconductor crystals, ultrafast laser-induced melting, photodisassociation and ultrafast solution dynamics of chemical species, and ultrafast internal rearrangements of the large organic molecule bacteriorhodopsin as photons absorbed in the retina initiate the first biochemical steps in the process of vision. The principles of ultrafast spectroscopy are covered in Chapter 9 with examples. Laser-Controlled Chemistry In a research area closely related to ultrafast spectroscopy, researchers are using specially engineered femtosecond laser waveforms to try to influence the course of photoinduced chemical reactions. In addition to observing ultrafast chemical motions as in time-resolved spectroscopy, the added idea here is to control the motions that take place. Since the intrinsic time scale for nuclear motions in chemical systems is tens to hundreds of femtoseconds, femtosecond laser pulses are a natural tool in pursuing the challenging goal of laser-controlled chemistry. Frequency Metrology Ultrashort pulses are usually emitted from lasers in the form of periodic trains, which under certain conditions can exhibit very high timing stability and long-term coherence. The spectrum of such a periodic train is a comb of up to hundreds of thousands of discrete spectral lines, which may be stabilized to permit precision measurements of optical frequencies with sub-hertz uncertainties across the optical spectrum. Such stabilized frequency combs are now widely adopted for high-precision frequency metrology and for investigations of precision optical clocks. Related topics are discussed in Section 7.5. High-Speed Electrical Testing Testing is a key issue in the development of high-speed electronic devices and circuits. Electronic test instrumentation based on established technology is usually slower than advanced high-speed research devices. However, since even the very fastest electronic devices only reach into the picosecond range, ultrafast laser technology offers speed to spare. Thus femtosecond optical pulses have been applied to generate subpicosecond electrical pulses and to measure operation of the highest-speed electronic devices. Ultrafast electrical pulse generation and measurement are discussed in Chapter 10. Laser–Plasma Interactions Lasers with intensities of 1013 W/cm2 and above (easily achieved using amplified femtosecond pulses) directed onto solid targets are sufficient to strip electrons from their nuclei, resulting in a laser-generated plasma. On the 100-fs time scale, the resulting free electrons do not have enough time to separate from the ionized nuclei. This provides the opportunity to study solid-density plasmas at temperatures as high as 1 million degrees. Short-Wavelength Generation High-intensity ultrashort pulses at visible wavelengths can also be used to generate coherent short-wavelength radiation in the vacuum ultraviolet and
4 INTRODUCTION AND REVIEW x-ray ranges through highly nonlinear harmonic generation processes or by pumping x-ray lasers.Coherent short-wavelength radiation may be important,for example,for imaging microscopic structures such as DNA. Optical Communications The low-loss transmission window of optical fibers has a band- width comparable to that of a 100-fs pulse,and therefore ultrashort-pulse technology may play an important role in optical communications.Subpicosecond pulses have already been used for laboratory experiments demonstrating fiber optic transmission of data at Tbit/s (1012 bit/s)rates.Here ultrafast optics technology is important not only for pulse gener- ation but also for signal processing,for data detection,and for the advanced metrology necessary for characterizing and optimizing ultrashort-pulse transmission [3,4].Ultrashort pulses may also prove important in wavelength-division-multiplexing(WDM)systems in which the fiber bandwidth is carved up into different wavelength bands or channels.For WDM applications it is the large bandwidth of the ultrashort pulse(not the short duration) which is useful,since a single pulse contains enough bandwidth to produce a number of wavelength channels. Biomedical Applications Ultrashort pulses are finding substantial applications in biomedi- cal imaging.Attractive features include the ability to perform optical imaging within scatter- ing media(e.g.,most tissues)and to obtain high-resolution depth information.An example of such an application is discussed in Section 3.3.3.In confocal microscopy significantly improved spatial resolution has been demonstrated by relying on two-photon excitation.The ability of ultrashort pulses to provide high intensity without high pulse energy is important in the use of this technique with sensitive biological samples.In laser-assisted surgical pro- cedures ultrashort pulses may in some cases reduce collateral tissue damage by reducing heat deposition. Materials Processing High-power lasers are used for a variety of industrial applications, such as cutting and drilling.With continuous-wave or"long"-pulse(nanoseconds)lasers, the minimum feature size and the quality of the cut are limited by thermal diffusion of heat to areas neighboring the laser focus.With femtosecond lasers,materials processing is possible using lower pulse energies,due to the very high peak powers,which lead to new physical mechanisms.This reduces the heat deposited into the sample during the laser machining process and leads to a much cleaner cutting or drilling operation. 1.2 BRIEF REVIEW OF ELECTROMAGNETICS Since ultrashort laser pulses are made up of light,and light is a form of electromagnetic radiation,we very briefly review Maxwell's equations,which describe all forms of electro- magnetic radiation,including light.We use MKS(SI)units here and throughout the book. It is assumed that the reader is already familiar with vector calculus.For a more detailed treatment of electromagnetics,the reader is directed to textbooks on this subject [5,6]. 1.2.1 Maxwell's Equations Maxwell's equations are a set of relationships between the electric field E and magnetic field H (boldface symbols denote vectors).Inside a medium we must also consider the
4 INTRODUCTION AND REVIEW x-ray ranges through highly nonlinear harmonic generation processes or by pumping x-ray lasers. Coherent short-wavelength radiation may be important, for example, for imaging microscopic structures such as DNA. Optical Communications The low-loss transmission window of optical fibers has a bandwidth comparable to that of a 100-fs pulse, and therefore ultrashort-pulse technology may play an important role in optical communications. Subpicosecond pulses have already been used for laboratory experiments demonstrating fiber optic transmission of data at Tbit/s (1012 bit/s) rates. Here ultrafast optics technology is important not only for pulse generation but also for signal processing, for data detection, and for the advanced metrology necessary for characterizing and optimizing ultrashort-pulse transmission [3,4]. Ultrashort pulses may also prove important in wavelength-division-multiplexing (WDM) systems in which the fiber bandwidth is carved up into different wavelength bands or channels. For WDM applications it is the large bandwidth of the ultrashort pulse (not the short duration) which is useful, since a single pulse contains enough bandwidth to produce a number of wavelength channels. Biomedical Applications Ultrashort pulses are finding substantial applications in biomedical imaging. Attractive features include the ability to perform optical imaging within scattering media (e.g., most tissues) and to obtain high-resolution depth information. An example of such an application is discussed in Section 3.3.3. In confocal microscopy significantly improved spatial resolution has been demonstrated by relying on two-photon excitation. The ability of ultrashort pulses to provide high intensity without high pulse energy is important in the use of this technique with sensitive biological samples. In laser-assisted surgical procedures ultrashort pulses may in some cases reduce collateral tissue damage by reducing heat deposition. Materials Processing High-power lasers are used for a variety of industrial applications, such as cutting and drilling. With continuous-wave or “long”-pulse (nanoseconds) lasers, the minimum feature size and the quality of the cut are limited by thermal diffusion of heat to areas neighboring the laser focus. With femtosecond lasers, materials processing is possible using lower pulse energies, due to the very high peak powers, which lead to new physical mechanisms. This reduces the heat deposited into the sample during the laser machining process and leads to a much cleaner cutting or drilling operation. 1.2 BRIEF REVIEW OF ELECTROMAGNETICS Since ultrashort laser pulses are made up of light, and light is a form of electromagnetic radiation, we very briefly review Maxwell’s equations, which describe all forms of electromagnetic radiation, including light. We use MKS (SI) units here and throughout the book. It is assumed that the reader is already familiar with vector calculus. For a more detailed treatment of electromagnetics, the reader is directed to textbooks on this subject [5,6]. 1.2.1 Maxwell’s Equations Maxwell’s equations are a set of relationships between the electric field E and magnetic field H (boldface symbols denote vectors). Inside a medium we must also consider the