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Annu. Rev. Phys. Chern. 1995. 46: 627-56 Copyright © 1995 by Annual Reviews Inc. All rights reserved
Annu. Rev. Phys. Chem. 1995.46:627-656. Downloaded from www.annualreviews.org Access provided by University of Manchester - John Rylands Library on 01/23/15. For personal use only.
FEMTOSECOND PULSE SHAPING, MULTIPLE-PULSE SPECTROSCOPY, AND OPTICAL CONTROL Hitoshi Kawashima, Marc M. Wefers, and Keith A. Nelson Department of Chemistry, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139 KEY WORDS:
coherence phenomena, optical waveform generation
ABSTRACT
review is presented of femtosecond pulse-shaping methods and their application to spectroscopy of atoms, molecules, and condensed materials. Pulse shaping can be used to generate femtosecond pulse sequences and other optical waveforms whose time-dependent amplitude, phase, frequency, and polarization profiles are all specified precisely. The light matter interaction mechanisms through which such waveforms can be used for optical control over molecular and material responses are discussed. Most of the spectroscopic experiments conducted to date that involve shaped femtosecond waveforms are reviewed. These have involved control over coherent electronic responses of atoms, small molecules, and multiple quantum wells and control over coherent molecular and lattice vibrations. A selective review is presented of theoretical predictions and qualitative discussions of optical control possibilities involving complex ultrafast waveforms. A
INTRODUCTION Since its development during the 1 980s, femtosecond spectroscopy has had as its primary aim the direct time-resolved observation of events that occur on ultrafast (i.e. subpicosecond) time scales following photo627 0066-426X/95/ 1 1 0 1 ·0627$05.00
Annu. Rev. Phys. Chem. 1995.46:627-656. Downloaded from www.annualreviews.org Access provided by University of Manchester - John Rylands Library on 01/23/15. For personal use only.
628
KAWASHIMA, WEFERS
& NELSON
excitation. Processes of interest have included many of the elementary collective and molecular processes in nature (1), such as lattice and molec ular vibrations, molecular rotations, and intermolecular vibrations ("col lisions") in liquids; electronic dephasing and relaxation in molecules, aggregates, semiconductors, and metals; collective rearrangements such as solid-liquid and solid-solid phase transitions; and chemical reactions in isolated molecules, biological systems, liquids, and solids. In nearly all cases, optical excitation has been conducted with a single femtosecond pulse or, at most, two pulses whose relative timing is controlled. In recent years, the objective of optical control over as well as obser vation of ultrafast events has become the focus of increasing attention. Of course, optical control over molecular or material behavior can be said to be exerted whenever the excitation wavelength, pulse duration, polar ization, or other properties are varied to elicit a desired sample response. In this sense optical control is a traditional, not novel, objective. From a technical point of view, the primary distinction of recent activity is that the degree of control over the ultrafast optical excitation field itself has reached unprecedented levels. Femtosecond "pulse-shaping" methods have been developed that permit the generation of specified waveforms whose time-dependent amplitude, phase, frequency, and polarization pro files may be specified. Thus samples whose responses to single pulses or other simple excitation fields may be very complex-including, for ex ample, motion along many degrees of freedom, wavepacket broadening or bifurcation among different channels, and entry into multiple reaction pathways-may be made to exhibit far simpler responses such as motion along a single mode, wavepacket propagation into minimum-uncertainty configurations, and reaction along a single chemical or even quantum mechanical pathway when subjected to a far more complex excitation field. This ability to control complex excitation gives rise to two substantial changes in the paradigm for spectroscopic experimentation, illustrated in Figure 1 . First, even in the context of the traditional spectroscopic objec tive of deducing the sample Hamiltonian that connects the excitation field to the sample response, the paradigm of deduction through analysis of a complex response changes to one of deduction through determination of the field required to elicit a simple, specified response. The best existing spectroscopic archetype for this paradigm is found in magnetic resonance, where the use of complex radio-frequency waveforms (and the ready access to the high-field regime, which is uncomplicated by unwanted nonlinear interactions) has yielded tractable responses from proteins and other extra ordinarily challenging samples. The second major change is in spec troscopic objective, which can be extended to include the generation of novel transient or long-lived species of fundamental or applied interest in
FEMTOSECOND PULSE-SHAPING AND CONTROLS
629
STANDARD PARADIGM
Annu. Rev. Phys. Chem. 1995.46:627-656. Downloaded from www.annualreviews.org Access provided by University of Manchester - John Rylands Library on 01/23/15. For personal use only.
NEW PARADIGM
....-� - ---,����� J\
����
Figure J
Schematic illustration of conventional and revised spectroscopic paradigms. In the former, a simple excitation field elicits a complex response from a complex sample. Analysis of the complex response is necessary to deduce the sample Hamiltonian. In the latter, complex excitation fields are tried and varied until a specific simple response is elicited. The Hamiltonian is deduced through iterative determination of which excitation field is necessary to produce the simple response. Use of complex excitation fields also makes possible the alternative objective of producing novel and potentially useful sample responses
with a high degree of control.
their own right. As indicated above, neither change represents a 1 00% new approach. Multiple resonant excitation fields, for example, have long been used to elicit sample responses that are more clearly defined than those resulting from single wavelengths, and photochemistry and optical fabrication techniques are widespread. However, the degree of complexity of the excitation fields and the control and fabrication objectives that may be realistically considered have undergone dramatic changes. To a considerable extent, theory and speculation about the possibilities for optical control-especially control over molecular behavior, including mode-selective chemistry-preceded and continue to outrace experimental capability for generation of the required optical waveforms. However, the technology for waveform generation is rapidly gaining ground, and spectroscopic exploitation has begun with a diverse range of atomic, molecular, and condensed matter objectives. These developments in femto second pulse shaping and its spectroscopic applications are the subjects of the present review. We begin with a brief outline of efforts at pulse shaping prior to those on femtosecond time scales. We then discuss methods for femtosecond pulse shaping and illustrate the degree of optical waveform specification now possible. Light-matter interactions through which controlled optical excitation has been conducted or discussed are summarized. Spectroscopic experiments conducted to date with femtosecond pulse-shaping tech niques, which are still few enough in number to permit rather com prehensive review, are then discussed. Theoretical treatment and con ceptual discussions of optical control possibilities are also reviewed, of
Annu. Rev. Phys. Chem. 1995.46:627-656. Downloaded from www.annualreviews.org Access provided by University of Manchester - John Rylands Library on 01/23/15. For personal use only.
630
KAWASHIMA, WEFERS & NELSON
necessity somewhat more selectively. A brief discussion of methods for characterization of ultrafast waveforms and sample responses to them is presented, and the review closes with a suggestion for the areas of greatest future challenge. There are important optical control possibilities not covered in this review. In particular, methods involving picosecond and slower time scales or continuous wave (cw) excitation are not discussed, except for the very cursory review of early pulse-shaping work that follows. Recent cw work involving quantum interferences (2--4) and their chemical effects (5) is not covered but has been reviewed elsewhere (5). Other reviews that overlap in content with this one are References 6-8.
FEMTOSECOND PULSE-SHAPING TECHNIQUES Early Developments: Nanosecond and Picosecond Time Scales Among the first experimental demonstrations of pulse shaping was the use amplitude and phase profiles were specified to control the corresponding amplitude and phase profiles of diffracted light (9). The time resolution was limited by the bandwidth of the acoustic signal generator, and optical waveforms with nanosecond or subnanosecond features were generated. With these techniques, magnetic resonance analogues, including photon echo (9, 10) and photon-locking experiments ( 1 1 ), were conducted for iodine molecules in the strong-field limit. Efforts were made to achieve subpicosecond time resolution through combination of acousto-optic or electro-optic pulse shaping on slower time scales with fiber-optic pulse compression ( 1 2a,b). Femtosecond fea tures were demonstrated, but this methodology has not advanced as far as the frequency-domain pulse-shaping approaches discussed below. of acousto-optic diffraction with an acoustic wave whose
Frequency-Domain Femtosecond Pulse Shaping Because the spectral and temporal profiles of transform-limited pulses are related through Fourier transformation, waveforms can be manipulated in either the time domain (13) (as described above) or in the frequency domain. The approaches should be equivalent, in principle, but for femto second pulses manipulation in the frequency domain is far more straight forward because the spectral width is large and high frequency resolution is unnecessary. A spectral filtering method developed originally for ultrafast optical communications applications (14-17) has proved extremely ver satile ( 1 8-20; MM Wefers & KA Nelson, unpublished data) and well suited for spectroscopy (22-24).
FEMTOSECOND PULSE-SHAPING AND CONTROLS
631
The method is illustrated in Figure 2. An ultrashort pulse is incident on a grating that angularly disperses the different frequency components. A subsequent lens focuses the different components onto different regions of a spatially varying mask. The mask can retard (change the optical path length of) and/or attenuate different frequency components, permitting
Annu. Rev. Phys. Chem. 1995.46:627-656. Downloaded from www.annualreviews.org Access provided by University of Manchester - John Rylands Library on 01/23/15. For personal use only.
manipUlation of the spectral phase and/or amplitude profiles. A second lens and grating recombine the spectrally filtered pulse, yielding a shaped waveform in the time domain. Originally, spectral filtering was done with permanent mask patterns, which were etched microlithographically onto glass substrates. This pro duces masks with excellent spatial resolution, but each desired waveform needed to be specified (weeks) in advance of its generation so that the appropriate mask pattern could be fabricated. For most spectroscopic applications, flexible on-the-spot generation of new waveforms is highly desirable. This was made possible through the use of a liquid crystal (LC) spatial light modulator (SLM) as a mask (16, 17). The pixels of the LC SLM can be addressed individually, so the mask is programmable and can
Grating
Figure 2
Lens
Double Mask
Lens
Grating
Schematic illustration of pulse-shaping apparatus (19).
Annu. Rev. Phys. Chem. 1995.46:627-656. Downloaded from www.annualreviews.org Access provided by University of Manchester - John Rylands Library on 01/23/15. For personal use only.
632
KAWASHIMA, WEFERS
& NELSON
be changed as needed for the generation of new waveforms. The LC mask demonstrated originally was used to variably retard the dispersed frequency components, i.e. as a phase mask. Two LC SLMs have since been used for phase and amplitude masks, first arranged in sequential two lens telescopes ( 1 8) and more recently as a single unit within a single telescope ( 1 9). In this latter version, the two LC SLMs are assembled into a single dual-mask unit whose two sets of pixels are precisely and permanently in register and angularly aligned. This offers many advantages in ease and accuracy of alignment and, in our view, has produced the best overall results to date in terms of versatility and waveform fidelity. In a recently demonstrated alternative method for spectral filtering (25), the two liquid crystal masks have been replaced by a single acousto-optic modulator in which (reminiscent of the earlier acousto-optic pulse-shaping method) the amplitude and phase profiles of the shaped optical waveform are determined by the corresponding acoustic-wave profiles. The prospects for this method are encouraging, but it is still in its preliminary stages. In the remainder of this section,results obtained through the use of LC SLMs are illustrated. The theoretical and experimental details of LC SLM pulse shaping have been described elsewhere (15, 1 7, 20,26). Figure 3 shows typical waveforms (solid curves) generated with the dual-mask unit, as measured by cross correlation with an unshaped 70-fs, 800-nm reference pulse. In all cases the time-dependent amplitude and phase profiles were simply specified to a computer that determined the appropriate mask patterns and generated them through its interface to the SLMs. Thus waveform generation is user friendly in the sense that the user need only indicate the desired waveform and need not calculate the mask pattern or understand the pulse-shaping technology in detail. Figure 3a illustrates an 800-fs optical square pulse. The structure on the top of the square pulse follows from the limited bandwidth of the input pulse. Optical square pulses may find applications in ultrafast all-optical switch ing (27). Figure 3b illustrates an equal-amplitude five-pulse sequence of 70-fs pulses in which the timing and the optical phases of the respective pulses have been specified. In this sequence the inter-pulse delay is gradu ally made smaller. Figure 3c shows a three-pulse sequence in which not only the timing and optical phases but also the time-dependent frequency profiles of the individual pulses are controlled. In this case the pulses are variably "chirped," i.e. their frequency components have been linearly displaced by a varying amount of time. The degree of chirp is reflected in the temporal broadening of each pulse. As illustrated below, chirped pulses and chirped pulse sequences can provide control over certain quantum systems (28-30). The waveform in Figure 3d is a sequence of 10 70-fs pulses with specified timings, amplitudes, and optical phases. This
633
FEMTOSECOND PULSE-SHAPING AND CONTROLS
b)
a)
�
0.8 �0.6 .�0.4 0.2
0.8 �0.6 .50.4 0.2 c: en
Annu. Rev. Phys. Chem. 1995.46:627-656. Downloaded from www.annualreviews.org Access provided by University of Manchester - John Rylands Library on 01/23/15. For personal use only.
c: en
a
0.8 .�0.6 .�0.4 0.2
-2
a -2
2
0
time in psec
�I
2
0
time in psec d)
c)
�0.8
·Iii g 0.6
c: en
o -2
-1
j
-1
\j
o
l
2
time in psec
.-"E 0.4 0.2 0
-2
0
time in psec
2
Figure 3 Time-dependent amplitude profiles of shaped waveforms, as determined through cross-correlations with an un shaped 70-fs pulse. The time-dependent phase profiles were also specified: (a) optical square pulse (b) 5 pulse sequences, (c) a 3-pulse sequence with different rates of chirp in each pulse, and (d) a lO-pulse sequence. The dashed curves in (c) and (d) indicate the specified amplitude profiles. ,
-
waveform, with its 10 independent features, tests the fidelity of the appar atus, because as the desired waveform becomes more complex, imper fections in alignment and calibration more clearly manifest themselves. The dashed curves in Figures 3c and 3d give the specified intensity profiles. All the desired waveforms are reproduced with excellent fidelity by those generated experimentally. The current dual-mask system can switch between different waveforms in about 2 s. Because of the sluggish relaxation times of the nematic LCs, the lower limit of this switching time is probably about 100 ms. Because the LC SLMs operate through controlled birefringence, they can also be used to generate waveforms with specified time-dependent polarization p rofile s For a completely arbitrary filter, four LC SLMs can be combined to provide independent control over spectral attenuation and spectral retardation for orthogonal polarizations. Using two masks, the .
634
KAWASHIMA, WEFERS
& NELSON
Annu. Rev. Phys. Chem. 1995.46:627-656. Downloaded from www.annualreviews.org Access provided by University of Manchester - John Rylands Library on 01/23/15. For personal use only.
spectral phases of orthogonal polarizations have been manipulated to produce waveforms with specified time-dependent polarizations (19). Such waveforms will be useful in controlling transient in optical birefringence and other anisotropic sample responses.
Other Pulse-Shaping Methods: Beamsplitting and Interferometry Methods based on partial reflection and interferometric recombination have been used to generate pairs of femtosecond pulses whose relative phases and delays are controlled. In this case the coarse relative delay between the two separated pulses is set with a standard delay line, and a fine relative delay, controlled piezoelectrically with precision that is better than the light wavelength, is used to set the relative phase (31, 32). The relative phase is evaluated by sending the two pulses into a third arm designed to eliminate the coarse temporal delay. The interference pattern (31) or the frequency spectrum (32) of the pulse pair, either of which is influenced by changes in the relative phase, is then analyzed to provide feedback and phase control.
Description of the Shaped Waveform The manner in which a shaped waveform is best described analytically at a particular point in space depends on which shaped features are to be emphasized. Two important examples are a sequence of pulses whose relative delays, phases, and amplitudes are controlled and a chirped pulse whose central frequency changes with time. In these cases, the electric field component Elt) polarized along direction i can be described in terms of a central frequency wand a slowly varying function clt), as follows: Elt) e;(t)
=
=
and
c;(t)
=
c,{t)e-iwt+c.c.;
L: Anei phases ¢n> and delays tn are specified. Equation Ic describes a pulse that is linearly chirped (i.e. whose central frequency changes linearly with time) at rate W. In general, two polarizations need to be specified independently.
FEMTOSECOND PULSE-SHAPING AND CONTROLS
635
EXCITATION MECHANISMS AND COHERENT STATES PRODUCED
Annu. Rev. Phys. Chem. 1995.46:627-656. Downloaded from www.annualreviews.org Access provided by University of Manchester - John Rylands Library on 01/23/15. For personal use only.
There are several optical excitation mechanisms whose use with femto second pulse shaping has been demonstrated or discussed. Impulsive stimulated Raman scattering (ISRS) (33), through which an ultrashort pulse experts a sudden ("impulsive") driving force on Raman-active vibrational modes, was used in the first spectroscopic application of femto second pulse shaping (22). One-photon optical absorption of visible light, through which electronic and excited-state vibrational coherences can
be induced, has also been used. We provide expressions for these two mechanisms. Additional possibilities that have been suggested and dis
cussed theoretically but not yet tried experimentally include the use of infrared and far-infrared (terahertz radiation) waveforms to manipulate polar vibrations of molecules (6) and the use of two-photon (34) or multi photon electronic absorption to gain spectroscopic aCcess to and manipu late wavepacket dynamics in otherwise "dark" states.
Single-Photon Electronic Absorption We are concerned below with resonant excitation of atoms, molecules, and condensed materials through single-photon transitions from the ground electronic state into an excited electronic state. The excited state may be isolated or may contain a manifold of sublevels. The Hamiltonian can be written as H
=
2.
O'lg> is the time-dependent state vector and Pj the transition dipole
moment.The light polarization is assumed to be linear and is not indicated The central optical frequency, co in Equation l a, is chosen to be equal to Wo. Equation 3 shows that for any excited states whose resonances are within the coherent bandwidth of an ultrashort excitation pulse, there will be significant coherent amplitudes, cj(t) ==
Further
Quick links to online content
Annu. Rev. Phys. Chern. 1995. 46: 627-56 Copyright © 1995 by Annual Reviews Inc. All rights reserved
Annu. Rev. Phys. Chem. 1995.46:627-656. Downloaded from www.annualreviews.org Access provided by University of Manchester - John Rylands Library on 01/23/15. For personal use only.
FEMTOSECOND PULSE SHAPING, MULTIPLE-PULSE SPECTROSCOPY, AND OPTICAL CONTROL Hitoshi Kawashima, Marc M. Wefers, and Keith A. Nelson Department of Chemistry, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139 KEY WORDS:
coherence phenomena, optical waveform generation
ABSTRACT
review is presented of femtosecond pulse-shaping methods and their application to spectroscopy of atoms, molecules, and condensed materials. Pulse shaping can be used to generate femtosecond pulse sequences and other optical waveforms whose time-dependent amplitude, phase, frequency, and polarization profiles are all specified precisely. The light matter interaction mechanisms through which such waveforms can be used for optical control over molecular and material responses are discussed. Most of the spectroscopic experiments conducted to date that involve shaped femtosecond waveforms are reviewed. These have involved control over coherent electronic responses of atoms, small molecules, and multiple quantum wells and control over coherent molecular and lattice vibrations. A selective review is presented of theoretical predictions and qualitative discussions of optical control possibilities involving complex ultrafast waveforms. A
INTRODUCTION Since its development during the 1 980s, femtosecond spectroscopy has had as its primary aim the direct time-resolved observation of events that occur on ultrafast (i.e. subpicosecond) time scales following photo627 0066-426X/95/ 1 1 0 1 ·0627$05.00
Annu. Rev. Phys. Chem. 1995.46:627-656. Downloaded from www.annualreviews.org Access provided by University of Manchester - John Rylands Library on 01/23/15. For personal use only.
628
KAWASHIMA, WEFERS
& NELSON
excitation. Processes of interest have included many of the elementary collective and molecular processes in nature (1), such as lattice and molec ular vibrations, molecular rotations, and intermolecular vibrations ("col lisions") in liquids; electronic dephasing and relaxation in molecules, aggregates, semiconductors, and metals; collective rearrangements such as solid-liquid and solid-solid phase transitions; and chemical reactions in isolated molecules, biological systems, liquids, and solids. In nearly all cases, optical excitation has been conducted with a single femtosecond pulse or, at most, two pulses whose relative timing is controlled. In recent years, the objective of optical control over as well as obser vation of ultrafast events has become the focus of increasing attention. Of course, optical control over molecular or material behavior can be said to be exerted whenever the excitation wavelength, pulse duration, polar ization, or other properties are varied to elicit a desired sample response. In this sense optical control is a traditional, not novel, objective. From a technical point of view, the primary distinction of recent activity is that the degree of control over the ultrafast optical excitation field itself has reached unprecedented levels. Femtosecond "pulse-shaping" methods have been developed that permit the generation of specified waveforms whose time-dependent amplitude, phase, frequency, and polarization pro files may be specified. Thus samples whose responses to single pulses or other simple excitation fields may be very complex-including, for ex ample, motion along many degrees of freedom, wavepacket broadening or bifurcation among different channels, and entry into multiple reaction pathways-may be made to exhibit far simpler responses such as motion along a single mode, wavepacket propagation into minimum-uncertainty configurations, and reaction along a single chemical or even quantum mechanical pathway when subjected to a far more complex excitation field. This ability to control complex excitation gives rise to two substantial changes in the paradigm for spectroscopic experimentation, illustrated in Figure 1 . First, even in the context of the traditional spectroscopic objec tive of deducing the sample Hamiltonian that connects the excitation field to the sample response, the paradigm of deduction through analysis of a complex response changes to one of deduction through determination of the field required to elicit a simple, specified response. The best existing spectroscopic archetype for this paradigm is found in magnetic resonance, where the use of complex radio-frequency waveforms (and the ready access to the high-field regime, which is uncomplicated by unwanted nonlinear interactions) has yielded tractable responses from proteins and other extra ordinarily challenging samples. The second major change is in spec troscopic objective, which can be extended to include the generation of novel transient or long-lived species of fundamental or applied interest in
FEMTOSECOND PULSE-SHAPING AND CONTROLS
629
STANDARD PARADIGM
Annu. Rev. Phys. Chem. 1995.46:627-656. Downloaded from www.annualreviews.org Access provided by University of Manchester - John Rylands Library on 01/23/15. For personal use only.
NEW PARADIGM
....-� - ---,����� J\
����
Figure J
Schematic illustration of conventional and revised spectroscopic paradigms. In the former, a simple excitation field elicits a complex response from a complex sample. Analysis of the complex response is necessary to deduce the sample Hamiltonian. In the latter, complex excitation fields are tried and varied until a specific simple response is elicited. The Hamiltonian is deduced through iterative determination of which excitation field is necessary to produce the simple response. Use of complex excitation fields also makes possible the alternative objective of producing novel and potentially useful sample responses
with a high degree of control.
their own right. As indicated above, neither change represents a 1 00% new approach. Multiple resonant excitation fields, for example, have long been used to elicit sample responses that are more clearly defined than those resulting from single wavelengths, and photochemistry and optical fabrication techniques are widespread. However, the degree of complexity of the excitation fields and the control and fabrication objectives that may be realistically considered have undergone dramatic changes. To a considerable extent, theory and speculation about the possibilities for optical control-especially control over molecular behavior, including mode-selective chemistry-preceded and continue to outrace experimental capability for generation of the required optical waveforms. However, the technology for waveform generation is rapidly gaining ground, and spectroscopic exploitation has begun with a diverse range of atomic, molecular, and condensed matter objectives. These developments in femto second pulse shaping and its spectroscopic applications are the subjects of the present review. We begin with a brief outline of efforts at pulse shaping prior to those on femtosecond time scales. We then discuss methods for femtosecond pulse shaping and illustrate the degree of optical waveform specification now possible. Light-matter interactions through which controlled optical excitation has been conducted or discussed are summarized. Spectroscopic experiments conducted to date with femtosecond pulse-shaping tech niques, which are still few enough in number to permit rather com prehensive review, are then discussed. Theoretical treatment and con ceptual discussions of optical control possibilities are also reviewed, of
Annu. Rev. Phys. Chem. 1995.46:627-656. Downloaded from www.annualreviews.org Access provided by University of Manchester - John Rylands Library on 01/23/15. For personal use only.
630
KAWASHIMA, WEFERS & NELSON
necessity somewhat more selectively. A brief discussion of methods for characterization of ultrafast waveforms and sample responses to them is presented, and the review closes with a suggestion for the areas of greatest future challenge. There are important optical control possibilities not covered in this review. In particular, methods involving picosecond and slower time scales or continuous wave (cw) excitation are not discussed, except for the very cursory review of early pulse-shaping work that follows. Recent cw work involving quantum interferences (2--4) and their chemical effects (5) is not covered but has been reviewed elsewhere (5). Other reviews that overlap in content with this one are References 6-8.
FEMTOSECOND PULSE-SHAPING TECHNIQUES Early Developments: Nanosecond and Picosecond Time Scales Among the first experimental demonstrations of pulse shaping was the use amplitude and phase profiles were specified to control the corresponding amplitude and phase profiles of diffracted light (9). The time resolution was limited by the bandwidth of the acoustic signal generator, and optical waveforms with nanosecond or subnanosecond features were generated. With these techniques, magnetic resonance analogues, including photon echo (9, 10) and photon-locking experiments ( 1 1 ), were conducted for iodine molecules in the strong-field limit. Efforts were made to achieve subpicosecond time resolution through combination of acousto-optic or electro-optic pulse shaping on slower time scales with fiber-optic pulse compression ( 1 2a,b). Femtosecond fea tures were demonstrated, but this methodology has not advanced as far as the frequency-domain pulse-shaping approaches discussed below. of acousto-optic diffraction with an acoustic wave whose
Frequency-Domain Femtosecond Pulse Shaping Because the spectral and temporal profiles of transform-limited pulses are related through Fourier transformation, waveforms can be manipulated in either the time domain (13) (as described above) or in the frequency domain. The approaches should be equivalent, in principle, but for femto second pulses manipulation in the frequency domain is far more straight forward because the spectral width is large and high frequency resolution is unnecessary. A spectral filtering method developed originally for ultrafast optical communications applications (14-17) has proved extremely ver satile ( 1 8-20; MM Wefers & KA Nelson, unpublished data) and well suited for spectroscopy (22-24).
FEMTOSECOND PULSE-SHAPING AND CONTROLS
631
The method is illustrated in Figure 2. An ultrashort pulse is incident on a grating that angularly disperses the different frequency components. A subsequent lens focuses the different components onto different regions of a spatially varying mask. The mask can retard (change the optical path length of) and/or attenuate different frequency components, permitting
Annu. Rev. Phys. Chem. 1995.46:627-656. Downloaded from www.annualreviews.org Access provided by University of Manchester - John Rylands Library on 01/23/15. For personal use only.
manipUlation of the spectral phase and/or amplitude profiles. A second lens and grating recombine the spectrally filtered pulse, yielding a shaped waveform in the time domain. Originally, spectral filtering was done with permanent mask patterns, which were etched microlithographically onto glass substrates. This pro duces masks with excellent spatial resolution, but each desired waveform needed to be specified (weeks) in advance of its generation so that the appropriate mask pattern could be fabricated. For most spectroscopic applications, flexible on-the-spot generation of new waveforms is highly desirable. This was made possible through the use of a liquid crystal (LC) spatial light modulator (SLM) as a mask (16, 17). The pixels of the LC SLM can be addressed individually, so the mask is programmable and can
Grating
Figure 2
Lens
Double Mask
Lens
Grating
Schematic illustration of pulse-shaping apparatus (19).
Annu. Rev. Phys. Chem. 1995.46:627-656. Downloaded from www.annualreviews.org Access provided by University of Manchester - John Rylands Library on 01/23/15. For personal use only.
632
KAWASHIMA, WEFERS
& NELSON
be changed as needed for the generation of new waveforms. The LC mask demonstrated originally was used to variably retard the dispersed frequency components, i.e. as a phase mask. Two LC SLMs have since been used for phase and amplitude masks, first arranged in sequential two lens telescopes ( 1 8) and more recently as a single unit within a single telescope ( 1 9). In this latter version, the two LC SLMs are assembled into a single dual-mask unit whose two sets of pixels are precisely and permanently in register and angularly aligned. This offers many advantages in ease and accuracy of alignment and, in our view, has produced the best overall results to date in terms of versatility and waveform fidelity. In a recently demonstrated alternative method for spectral filtering (25), the two liquid crystal masks have been replaced by a single acousto-optic modulator in which (reminiscent of the earlier acousto-optic pulse-shaping method) the amplitude and phase profiles of the shaped optical waveform are determined by the corresponding acoustic-wave profiles. The prospects for this method are encouraging, but it is still in its preliminary stages. In the remainder of this section,results obtained through the use of LC SLMs are illustrated. The theoretical and experimental details of LC SLM pulse shaping have been described elsewhere (15, 1 7, 20,26). Figure 3 shows typical waveforms (solid curves) generated with the dual-mask unit, as measured by cross correlation with an unshaped 70-fs, 800-nm reference pulse. In all cases the time-dependent amplitude and phase profiles were simply specified to a computer that determined the appropriate mask patterns and generated them through its interface to the SLMs. Thus waveform generation is user friendly in the sense that the user need only indicate the desired waveform and need not calculate the mask pattern or understand the pulse-shaping technology in detail. Figure 3a illustrates an 800-fs optical square pulse. The structure on the top of the square pulse follows from the limited bandwidth of the input pulse. Optical square pulses may find applications in ultrafast all-optical switch ing (27). Figure 3b illustrates an equal-amplitude five-pulse sequence of 70-fs pulses in which the timing and the optical phases of the respective pulses have been specified. In this sequence the inter-pulse delay is gradu ally made smaller. Figure 3c shows a three-pulse sequence in which not only the timing and optical phases but also the time-dependent frequency profiles of the individual pulses are controlled. In this case the pulses are variably "chirped," i.e. their frequency components have been linearly displaced by a varying amount of time. The degree of chirp is reflected in the temporal broadening of each pulse. As illustrated below, chirped pulses and chirped pulse sequences can provide control over certain quantum systems (28-30). The waveform in Figure 3d is a sequence of 10 70-fs pulses with specified timings, amplitudes, and optical phases. This
633
FEMTOSECOND PULSE-SHAPING AND CONTROLS
b)
a)
�
0.8 �0.6 .�0.4 0.2
0.8 �0.6 .50.4 0.2 c: en
Annu. Rev. Phys. Chem. 1995.46:627-656. Downloaded from www.annualreviews.org Access provided by University of Manchester - John Rylands Library on 01/23/15. For personal use only.
c: en
a
0.8 .�0.6 .�0.4 0.2
-2
a -2
2
0
time in psec
�I
2
0
time in psec d)
c)
�0.8
·Iii g 0.6
c: en
o -2
-1
j
-1
\j
o
l
2
time in psec
.-"E 0.4 0.2 0
-2
0
time in psec
2
Figure 3 Time-dependent amplitude profiles of shaped waveforms, as determined through cross-correlations with an un shaped 70-fs pulse. The time-dependent phase profiles were also specified: (a) optical square pulse (b) 5 pulse sequences, (c) a 3-pulse sequence with different rates of chirp in each pulse, and (d) a lO-pulse sequence. The dashed curves in (c) and (d) indicate the specified amplitude profiles. ,
-
waveform, with its 10 independent features, tests the fidelity of the appar atus, because as the desired waveform becomes more complex, imper fections in alignment and calibration more clearly manifest themselves. The dashed curves in Figures 3c and 3d give the specified intensity profiles. All the desired waveforms are reproduced with excellent fidelity by those generated experimentally. The current dual-mask system can switch between different waveforms in about 2 s. Because of the sluggish relaxation times of the nematic LCs, the lower limit of this switching time is probably about 100 ms. Because the LC SLMs operate through controlled birefringence, they can also be used to generate waveforms with specified time-dependent polarization p rofile s For a completely arbitrary filter, four LC SLMs can be combined to provide independent control over spectral attenuation and spectral retardation for orthogonal polarizations. Using two masks, the .
634
KAWASHIMA, WEFERS
& NELSON
Annu. Rev. Phys. Chem. 1995.46:627-656. Downloaded from www.annualreviews.org Access provided by University of Manchester - John Rylands Library on 01/23/15. For personal use only.
spectral phases of orthogonal polarizations have been manipulated to produce waveforms with specified time-dependent polarizations (19). Such waveforms will be useful in controlling transient in optical birefringence and other anisotropic sample responses.
Other Pulse-Shaping Methods: Beamsplitting and Interferometry Methods based on partial reflection and interferometric recombination have been used to generate pairs of femtosecond pulses whose relative phases and delays are controlled. In this case the coarse relative delay between the two separated pulses is set with a standard delay line, and a fine relative delay, controlled piezoelectrically with precision that is better than the light wavelength, is used to set the relative phase (31, 32). The relative phase is evaluated by sending the two pulses into a third arm designed to eliminate the coarse temporal delay. The interference pattern (31) or the frequency spectrum (32) of the pulse pair, either of which is influenced by changes in the relative phase, is then analyzed to provide feedback and phase control.
Description of the Shaped Waveform The manner in which a shaped waveform is best described analytically at a particular point in space depends on which shaped features are to be emphasized. Two important examples are a sequence of pulses whose relative delays, phases, and amplitudes are controlled and a chirped pulse whose central frequency changes with time. In these cases, the electric field component Elt) polarized along direction i can be described in terms of a central frequency wand a slowly varying function clt), as follows: Elt) e;(t)
=
=
and
c;(t)
=
c,{t)e-iwt+c.c.;
L: Anei phases ¢n> and delays tn are specified. Equation Ic describes a pulse that is linearly chirped (i.e. whose central frequency changes linearly with time) at rate W. In general, two polarizations need to be specified independently.
FEMTOSECOND PULSE-SHAPING AND CONTROLS
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EXCITATION MECHANISMS AND COHERENT STATES PRODUCED
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There are several optical excitation mechanisms whose use with femto second pulse shaping has been demonstrated or discussed. Impulsive stimulated Raman scattering (ISRS) (33), through which an ultrashort pulse experts a sudden ("impulsive") driving force on Raman-active vibrational modes, was used in the first spectroscopic application of femto second pulse shaping (22). One-photon optical absorption of visible light, through which electronic and excited-state vibrational coherences can
be induced, has also been used. We provide expressions for these two mechanisms. Additional possibilities that have been suggested and dis
cussed theoretically but not yet tried experimentally include the use of infrared and far-infrared (terahertz radiation) waveforms to manipulate polar vibrations of molecules (6) and the use of two-photon (34) or multi photon electronic absorption to gain spectroscopic aCcess to and manipu late wavepacket dynamics in otherwise "dark" states.
Single-Photon Electronic Absorption We are concerned below with resonant excitation of atoms, molecules, and condensed materials through single-photon transitions from the ground electronic state into an excited electronic state. The excited state may be isolated or may contain a manifold of sublevels. The Hamiltonian can be written as H
=
2.
O'lg> is the time-dependent state vector and Pj the transition dipole
moment.The light polarization is assumed to be linear and is not indicated The central optical frequency, co in Equation l a, is chosen to be equal to Wo. Equation 3 shows that for any excited states whose resonances are within the coherent bandwidth of an ultrashort excitation pulse, there will be significant coherent amplitudes, cj(t) ==
