F RONTIERS IN O PTICS REVIEW Frontiers in Ultrashort Pulse Generation: Pushing the Limits in Linear and Nonlinear G. Steinmeyer,* D. H. Sutter, L. Gallmann, N. Matuschek, U. Keller

Optical pulses in the 5- range are produced by a variety of The Kerr Effect, , and methods. Although different in technical detail, each method relies on the Pulse Compression same three key components: spectral broadening due to the nonlinear At high intensities, the polarization inside a optical Kerr effect, dispersion control, and ultrabroadband amplification. dielectric medium does not proportionally fol- The state of the art of ultrashort pulse generation is reviewed with a focus low the electric field, and a nonlinear compo- on direct oscillator schemes. nent at the frequency of the exciting is induced, giving rise to an instantaneous change Our ability to perceive the dynamics of nature ton absorption, is used to form the product of the n proportional to the is ultimately limited by the temporal resolu- of the two replicas, which depends on the time- and space-dependent intensity I(t, xជ) tion of the instruments available to us. Me- temporal overlap of the replicas. Effective- ͑ ជ͒ ϭ ϩ ͑ ជ͒ chanical shutters allow for resolution in the ly, this allows converting measurement of a n t, x n0 n2I t, x (1) millisecond range, whereas stroboscopic illu- time into the measurement of a distance. This is called the optical Kerr effect (11), which mination allows us to probe the microsecond Examples of measurements is essential for all the concepts delivering pulses range. Modern electronic sampling oscillo- of some of the shortest pulses generated to in the two-cycle regime. For typical solid-state scopes eventually brought the limit down into date are shown (Fig. 2). Although com- materials, the nonlinear index n2 is on the order the picosecond range. Ultrafast have pletely different pulse generation tech- of several 10Ϫ16 cm2/W. The index change advanced the temporal resolution of measure- niques were employed in these examples, causes a temporal delay or phase shift for the ments another three orders of magnitude into the autocorrelation traces are very similar, most intense parts of a beam. Assuming Gauss- the sub–10-fs (1 fs ϭ 10Ϫ15 s) regime, allow- as indicated by the relative magnitude of ian spatial and temporal profiles, the effects ing for the direct observation of vibrational the first- and second-side maximum of the caused by this index change are shown (Fig. 3) molecular dynamics (1). The broad spectral traces shown. longitudinal and transverse to the propagation content can be used in medical diagnostics Here, we describe methods that can be direction. Retardation of the most intense part (2), and the extreme concentration of energy used to generate pulses as short as those of a plane wavefront transversely acts like a in femtosecond pulses is useful for material displayed in Fig. 2, with a full width at half focusing lens, whereas along the axis of prop- processing because much finer structures can maximum of only about 5 fs (6–10). For a agation, the Kerr effect retards the center of an be created in the absence of thermal interac- wavelength in the visible or near- optical pulse. This longitudinal effect produces tion caused by longer pulses (3). spectral range, as in the examples we discuss, a red shift of the leading part of the pulse, and Figure 1 shows the historical development this corresponds to about two optical cycles. a blue shift in the trailing part and has also been of ultrafast pulse generation. In the late We will show that pulse generation tech- named self-phase modulation (SPM). It is im- 1980s, the pulse duration of dye lasers was as niques demonstrated in the two-cycle regime portant to note that SPM generates extra band- low as 27 fs (4), which was later compressed rely essentially on three identical ingredients: width, that is, it spectrally broadens the pulse. to6fs(5). At a wavelength of 600 nm, only the nonlinear optical Kerr effect acting as a SPM alone does not modify the pulse enve- three optical cycles fit under the full width at spectral broadening process, precise control lope, but a much shorter pulse can be created half maximum of the intensity envelope of of dispersion, and an ultrabroadband ampli- with the extra bandwidth generated, as follows such a pulse. It took almost a decade to fying process. Here, we review these key from the of the wider spec- surpass these results with solid-state lasers. ingredients comprehensively and focus on the trum. To exploit the broadened bandwidth for Our goal is to review this recent progress interaction between nonlinear pulse-shaping the generation of a shorter pulse, the red and with ultrafast solid-state lasers. processes and linear phase correction. We blue components in the temporal wings of the Measurement of ultrashort pulses is also emphasize how these effects can be used pulse have to be temporarily delayed and ad- a demanding task. Whereas traditionally, a inside a laser to directly generate extremely vanced, respectively. The spectral dependence short event has been characterized with the short pulses. of the speed of light needed to shorten the aid of an even shorter event, this is not an option for the characterization of the short- Fig. 1. Development of shortest est event. Nonlinear autocorrelation tech- reported pulse duration over the niques have been used in ultrafast optics last three decades. Circles refer to because they use a short event to measure dye-laser technology, triangles re- itself. In this type of measurement, two fer to Ti:sapphire laser systems. Filled symbols indicate results di- replicas of the pulse are generated, which rectly achieved from an oscillator, are delayed with respect to each other. An open symbols indicate results instantaneous nonlinear optical effect, such achieved with additional external as second-harmonic generation or two-pho- pulse compression.

Institute of Quantum Electronics, Swiss Federal Insti- tute of Technology, ETH Ho¨nggerberg, HPT, CH-8093 Zu¨rich, Switzerland. *To whom correspondence should be addressed. E- mail: [email protected]

www.sciencemag.org SCIENCE VOL 286 19 NOVEMBER 1999 1507 F RONTIERS IN O PTICS spectrally broadened pulse is called dispersion, where c is the speed of light in vacuum, and gives rise to solitons, optical pulses that are ␻ which is a linear optical effect independent of 0 is a reference frequency for series expan- able to propagate for long distances in a intensity. For a given optical element with sion. The first coefficient (i ϭ 1 in Eq. 2) in nonlinear medium with either a constant or a ␻ץ ␻ ץ ᐉ length , dispersion manifests itself as a spec- this dispersion series Tg( 0)/ is also periodically changing pulse shape (11, 12). trally dependent propagation time. Spectral called group delay dispersion (GDD), which Ultimately, compression schemes are lim- components at (angular) frequency ␻ are de- is a function of reference frequency. A care- ited by higher-order dispersion (terms with layed by a group delay ful balance between frequency dependence i Ͼ 1 in Eq. 2) and parasitic nonlinearities. given by dispersion and time dependence giv- For pulses shorter than 100 fs, compression is :en by nonlinearity of the refractive index n is typically limited to factors of less than 10 ץ ᐉ T ͑␻͒ ϭ ͑␻n͒ ␻ needed for efficient compression of a pulse. Dye laser pulses with 50 fs duration haveץ g c In most compression schemes, nonlinearity been compressed down to 6 fs (5). Similar ϱ iT and dispersion are supplied in two successive concepts have been used for external pulseץ 1 ϭ ͸ gͯ ͑␻ Ϫ ␻ ͒i -␻i 0 (2) steps, but optical fibers in the infrared pro- compression of 13-fs pulses from a Ti:sapץ i! ␻ i ϭ 0 0 vide these two effects simultaneously. This phire laser (9) and of 20-fs pulses from a Ti:sapphire laser amplifier (10), resulting in both cases in approximately 4.5-fs pulses Fig. 2. Comparison of inter- ferometric autocorrelation (Fig. 2). The use of a hollow fiber filled with traces of different pulse a noble gas resulted in unsurpassed pulse sources in the 5-fs range. (A) energies of about 0.5 mJ with 5.2-fs pulses Optical parametric amplifica- and a peak power of 0.1 TW (13). tion (8), (B) compression of cavity-dumped pulses in a sil- Saturable Absorbers and Passive ica fiber (9), (C) compression Mode-Locking of microjoule pulses in a hol- low fiber filled with krypton A compression scheme can be directly inte- (10), and (D) pulses from a grated into a laser. In this section, we de- Ti:sapphire oscillator (7). scribe how to place a suitable nonlinear op- Dots in (A) through (D) and tical device in the feedback loop of the laser lines in (A) refer to measured oscillator to directly support short-pulse op- data, lines in (B) through (D) indicate the fit that was used eration (Fig. 4A). Traditionally, this type of to estimate pulse duration operation of a laser has often been considered from the autocorrelation. in the frequency domain (14). In this picture, the eigenfrequencies (or longitudinal modes) of the cavity have to be phase-locked to generate a short pulse. An amplitude modu- lator inside the cavity phase-locks these lon- gitudinal modes when the modulation fre- quency is equal to the frequency spacing of the modes. This type of operation has been named mode-locking. In the time-domain picture, mode-locking means that the ampli- tude modulator opens and closes synchro- nously with the light propagating through the cavity. The modulator can either be driven by an external signal source (active mode-lock- ing) or directly by the optical pulses inside the laser cavity (passive mode-locking). Here, we restrict ourselves to the latter meth- od because it delivers the shortest pulses. The goal is to phase-lock as many longitudinal modes as possible because the broader the phase-locked spectrum the shorter the pulse that can be generated. The passive amplitude modulator is a sat- urable absorber which has an increased trans- mission or reflection for high peak powers and produces a self-amplitude modulation (SAM). This SAM reduces the losses for short-pulse operation of a laser. An optical pulse traveling through a saturable absorber in a solid-state laser is shortened by the SAM, provided the response time of the absorber is sufficiently fast. In a mode-locked laser, Fig. 3. The Kerr effect gives rise to an increase of the refractive index with intensity, causing a pulse formation should start from normal retardation of the most intense parts of a pulse. In its longitudinal form (A), the Kerr effect causes self-phase modulation; in its transverse form (B), a nonlinear lens is formed in the central part of noise fluctuations in the laser to initiate the beam profile. mode-locking. In the steady-state femtosec-

1508 19 NOVEMBER 1999 VOL 286 SCIENCE www.sciencemag.org F RONTIERS IN O PTICS ond regime, dispersion and bandwidth limi- laser (20), pulses compressed by the the sub–10-fs regime however, pulse-shaping tation of the gain medium, mirrors, and so effects in the coupled cavity are directly cou- processes become very complex (28), and forth mainly cause temporal stretching of the pled back into the main laser cavity. This significant deviations from this simple theo- pulse. Therefore, the pulse shortening effect provides more gain for the center of the pulse. retical picture are observed. must be dominant for pulse durations ranging At 1.5 ␮m, pulses as short as four optical The Kerr effect is strong enough to sustain from nanoseconds at start-up to cycles or 19 fs have been demonstrated with mode-locking but is typically unable to initi- at steady-state operation. color center lasers (21). Later, the SPM-to- ate it. To overcome this limitation, an ultra- Traditionally, dyes have been used as sat- SAM conversion with a coupled cavity was broadband SESAM can be used to reliably urable absorbers for passive mode-locking. demonstrated for a case where no soliton start KLM (7). With the additional stabiliza- Today in solid-state lasers, dyes have either effects were present (22). In this case, an tion mechanism provided by the SESAM, been replaced by saturable absorbers ob- uncompressed pulse was fed back into the resonator alignment constraints required for tained by Kerr or semiconductor nonlineari- main cavity. An effective SAM was obtained pure KLM are considerably relaxed. There- ties. The precise control of optical nonlineari- because SPM inside the coupled cavity gen- fore, use of the SESAM results in a cleaner ties, combined with the availability of a va- erates a phase modulation on the pulse (Fig. spatial mode pattern (Fig. 5). This example riety of bandgaps ranging from the visible to 3) that adds constructively at the peak of the shows how suitable nonlinear optical effects the infrared, makes semiconductor materials pulse in the main cavity and destructively in can be used in a combination of saturable very attractive for use as saturable absorbers the temporal wings, thus shortening the pulse absorbers that covers several orders of mag- in solid-state lasers (15). Semiconductor ma- duration inside the main cavity. This is re- nitude of pulse duration, decoupling start-up terials typically provide an optical nonlinear- ferred to as additive-pulse mode-locking and steady-state pulse formation. ity with two pronounced time constants. In- (APM) (23). Although very powerful in prin- traband processes give rise to a very rapid ciple, these coupled-cavity schemes have the Continuum-Generation and relaxation in the 100-fs regime, while elec- severe disadvantage that the auxiliary cavity Amplification-Based Schemes tron-hole recombination generates a slow re- has to be stabilized interferometrically. Independent from the generation of ultrashort sponse time in the picosecond regime. The An alternative method for converting the pulses directly from a laser oscillator, there slow response time can be reduced by several reactive Kerr nonlinearity into an effective are schemes that generate even shorter pulses orders of magnitude with low-temperature saturable absorber has been discovered in the by using pulse compression outside a cavity epitaxy (16). Such semiconductors grown at Ti:sapphire laser: Kerr-lens mode-locking with either standard glass fibers (9) or noble- low temperatures are markedly different from (KLM) (24). In KLM, the transverse Kerr gas filled, hollow fibers (10), and by optical normally grown materials, exhibiting an in- effect produces a nonlinear lens (Fig. 3) that parametric amplification of white-light con- crease in trap densities and decrease in carrier focuses the high-intensity part of the beam tinuum pulses (8). These schemes rely on lifetimes of four orders of magnitude. The more strongly than the low-intensity part. white-light continuum generation, which was ability to artificially vary such parameters Combined with an intracavity aperture, the first observed with orange amplified dye laser allowed a systematic study of pulse genera- Kerr lens produces less loss for high intensi- pulses (29). The resulting spectrally broad- tion. Typically, a semiconductor saturable ab- ties and forms an effective fast saturable ab- ened pulses spanned over the entire visible sorber is integrated directly into a mirror sorber (25). In this configuration, the Kerr range. Structurally, there is an important dif- structure, resulting in a device whose reflec- lens is most efficiently used for pulse forma- ference between the compression/amplifica- tivity increases as the incident optical inten- tion if the cavity is configured to support only tion schemes (Fig. 4, B and C) and the direct sity increases. This general class of devices is pulsed operation and to prohibit continuous generation in an oscillator (Fig. 4A). Whereas called semiconductor saturable absorber mir- operation of the laser. A concise account of the direct approach of generating pulses in- rors (SESAMs) (15). With SESAMs, all im- the SAM produced by the Kerr lens in differ- side the oscillator performs all steps inside portant saturable absorber parameters, such ent cavity regimes can be found in (26). The the laser feedback loop, the other approaches as response time, saturation fluence, and longitudinal Kerr effect also contributes to put all processes into a linear sequence. modulation depth, can be adapted over sev- the pulse-shaping action inside the cavity, Continuum-based schemes start with puls- eral orders of magnitude. This allowed for the which is well known and has been used be- es from a Ti:sapphire oscillator, which are first demonstration of self-starting and stable fore in dye lasers. To a good approximation, typically amplified to Ͼ100 ␮J pulse energy. passive mode-locking of diode-pumped sol- the interplay of linear and nonlinear pulse- To date, spectral filtering due to the limited id-state lasers with intracavity saturable ab- shaping effects has been explained theoreti- bandwidth of the gain material has prohibited sorbers (17). The mirror structure can be cally using Haus’ master equation (27). This the direct generation of amplified pulses with manufactured using semiconductor materials aproximation works well for longer pulses. In less than 16 fs duration (30). To achieve a (for example, AlAs/AlGaAs), standard di- electric coating materials, or a metal coating. So far, metal mirror–based SESAMs demon- Fig. 4. Different combina- strate the largest bandwidth but also limit the tions of amplification, the average output power (18). Schemes using Kerr effect, and dispersion used for the generation of broadband AlGaAs/CaF2 Bragg mirrors are pulses in the two-cycle regime: being considered as well (19). (A) directly in an oscillator, (B) The extremely rapid response and the using external compression in broad bandwidth of the Kerr nonlinearity are hollow, gas-filled fibers or very attractive for a mode-locking process. fused silica fibers, and (C) con- One way of using the phase nonlinearity of tinuum generation in sapphire and subsequent parametric the Kerr effect for mode-locking is to convert amplification. SPM into an effective amplitude nonlinearity, that is, a SAM. The earliest mode-locking schemes based on SPM exclusively used a coupled cavity for this purpose. In the soliton

www.sciencemag.org SCIENCE VOL 286 19 NOVEMBER 1999 1509 F RONTIERS IN O PTICS bandwidth supporting two-cycle pulses, SPM metric process, each pump photon is split into (36). For shorter pulse operation, higher or- is employed by focusing the amplified pulses two photons, with the sum of the generated der dispersion has to be compensated for. into a nonlinear optical medium. photon energies equal to the pump photon Specially designed mirrors can also be Noble gases such as Ar or He provide SPM energy. If photons within the wavelength used for dispersion compensation. Standard with minimal dispersion. With no vibrational range of the parametric process are provided dielectric mirrors are composed of identical infrared resonance present, noble gases provide as a seed, they will be amplified in the non- quarter-wave layer pairs and provide high much flatter spectral dispersion than bulk ma- linear crystal. The seed pulse is derived from reflectance over a range of about 25% of the terials if the same amount of SPM is desired. white-light continuum generation. Broadband central wavelength, depending on the refrac- Additionally, they are not subject to the Raman parametric amplification produced pulses tive index contrast of the layer materials em- effect, which poses another limit to the useful- with a duration of Ͻ5fs(8). Pumped by a ployed. Outside this region, these simple mir- ness of nonlinear optical materials for SPM- frequency-doubled pulse from a Ti:sapphire ror structures have considerable transmission. based pulse compression. Because SPM is also amplifier system, optical parametric amplifi- Special mirrors for dispersion compensation much weaker in gases than in bulk media, ers (OPAs) generate sub–10-fs duration in the can be obtained by stacking quarter-wave higher intensities or longer interaction lengths spectral range from 550 to 780 nm. An OPA layers optimized for different center wave- are typically required, which is suitably provid- system has been developed with microjoule lengths, such that long wavelengths are made ed in a strongly confined hollow-fiber geometry pulses tunable from 1.1 to 2.6 ␮m and pulse to penetrate deeper into the mirror structure (31). Use of hollow fibers for pulse compres- durations as short as 14.5 fs (33). than short wavelengths as illustrated in Fig. sion has produced pulses of about 4.5 fs dura- Parametric conversion gives access to 6A. Such mirrors are called chirped mirrors tion. Nevertheless, similar pulse durations have two-cycle pulses outside the spectral range of and the wavelength-dependent penetration been obtained in the 100-nJ pulse energy re- Ti:sapphire. Combination of several OPA depth provides the desired dispersion to com- gime with standard optical fibers (9). The direct processes seeded by the same continuum pensate for material effects (37). In addition use with oscillators has not yet been demon- pulse allows the simultaneous generation of to dispersion compensation, chirped mirrors strated, and it remains to be seen how far non- coherent radiation over the entire spectrum also give a much broader reflection band- linear optical materials can be optimized and from 400 nm to 1.5 ␮m. This spectrum could width than standard mirrors. engineered for pulse compression purposes. potentially produce a single-cycle pulse (34), A major problem in chirped mirror design Frequency-conversion in nonlinear optical provided that dispersion compensation over arises due to multiple reflections between the crystals can also be used for the generation of such a broad range is accomplished. All con- chirped mirror structure and the top layer of two-cycle pulses. Of particular interest are tinuum-based schemes require precise disper- the coating. The strong index discontinuity at so-called parametric processes, which have sion control, which in all cases demonstrated this interface gives rise to unwanted interfer- been demonstrated with amplification band- has been achieved using specially designed ence, which results in oscillations of the widths of up to 150 THz (32). In the para- mirrors and prism sequences. group delay with wavelength. Double- chirped mirrors (DCMs) were developed to Dispersion Compensation reduce such detrimental dispersion oscilla- Limited control of the intracavity dispersion tions (38). Figure 6B shows the spectrally is the main obstacle in the generation of dependent penetration of the electromagnetic extremely short pulses. For optimum pulse field into a broadband DCM coating. Reflec- formation in a KLM laser, a small but con- tivity and dispersion characteristics of a stant intracavity dispersion is required over DCM used in a Ti:sapphire oscillator are the full spectral content of the pulse (27). In shown in Fig. 7, A and B, respectively. For a typical sub–10-fs Ti:sapphire laser, the un- comparison, the gain curve of Ti:sapphire is compensated round-trip GDD caused by the also shown in Fig. 7A. laser crystal alone amounts to more than 100 The chirped mirror technology strongly re- fs delay between the long- and short-wave- duces higher-order dispersion contributions in- length components covered by the gain ma- side the cavity and makes bandwidths up to 200 terial. To compensate for this group-delay THz accessible for pulse generation. On a glob- dispersion (Eq. 2), a component with the al wavelength scale, compensation is nearly opposite sign of dispersion has to be inserted perfect, yielding a small average value of the into the cavity. Between these sections of GDD. On a local scale, the mirrors introduce opposite sign of GDD, the pulse width will be residual group delay oscillations with periods of periodically stretched and recompressed from several tens of nanometers (Fig. 7B). The mag- the sub–10-fs to the 100-fs range. nitude of these residual dispersion oscillations Different schemes for providing disper- increases with the bandwidth of the mirrors. For sion to compensate for material effects and carefully optimized broadband DCMs, the self-phase modulation inside a laser cavity peak-to-peak amplitude of these oscillations has have been proposed. The been reduced to less than 1 fs per reflection, (35) is the most often employed scheme and resulting in the small measured phase oscilla- Fig. 5. Visible part of the spatial beam profiles behind one intracavity mirror of a two-cycle introduces adjustable dispersion. However, tion of the laser pulses shown in Fig. 7B. The Ti:sapphire laser. (A) Cavity parameters are generally it is only possible to compensate combined action of SPM and dispersion pro- close to the stability limit, with pure KLM ac- dispersion to the second order of Eq. 2 with a vides a means of energy transfer within the tion. (B) Cavity is adjusted for a reduced KLM- prism pair. For optimum performance of a pulse spectrum inside a mode-locked laser. Ef- effect with stronger stabilization action from laser, the prism material has to be carefully fectively, this concentrates energy at the mini- the SESAM. Note the clearly visible yellow chosen and the total amount of material in- ma of the group delay oscillations (39) as indi- spectral content caused by SPM in the gain material, extending well beyond the Ti:sapphire side the cavity should be kept at a minimum. cated by the strongly modulated spectra typical gain bandwidth. Pictures were taken on Pulse durations of about 8.5 fs have been of sub–10-fs laser pulses; the pulse shape is 100ASA slide film (Kodak Elite). demonstrated using only prism compensation strongly affected by the dispersion oscilla-

1510 19 NOVEMBER 1999 VOL 286 SCIENCE www.sciencemag.org F RONTIERS IN O PTICS tions and significantly deviates from the sim- uses the autocorrelation data together with characterized in amplitude and phase (7, 46). ple picture predicted from the soliton-like the fundamental spectrum (9, 44) to provide In these measurements, the residual uncom- pulse shaping (7, 40). Moreover, group delay a simultaneous fit to both measurements. pensated dispersion mainly due to the output- oscillations can ultimately limit the intracav- Whereas the characterization techniques dis- coupling mirror of the laser is clearly visible ity bandwidth and the shortest achievable cussed so far require the use of an iterative (Fig. 7B). The small oscillation in the central pulse width. Chirped mirrors with shifted fitting algorithm to retrieve the phase, part of the spectrum stems from dispersion dispersion characteristics can be combined to SPIDER (spectral phase interferometry for oscillations of the double-chirped mirrors. reduce the total intracavity group delay oscil- direct electric-field reconstruction) allows for The advances in measurement tools have lations. Current research is directed to pro- fast, noniterative reconstruction of the pulse clearly contributed to the success of generat- vide even broader bandwidth without detri- from the measurement of two spectra (45). ing shorter and shorter pulses. mental dispersion oscillations. Phase-sensitive techniques have been used Two different philosophies about the use extensively to characterize femtosecond laser Conclusion and Outlook of chirped mirrors have evolved. On the one sources and, apart from being more accurate, Comparison of the different techniques that hand, exclusive use of mirrors allows for very give more insight into the complex pulse currently allow for pulses in the two-cycle compact dispersion compensation schemes, dynamics of sub–10-fs pulses. regime identifies three essential mechanisms: which is of particular importance for oscilla- Baltuska et al. designed their dispersion an ultrafast spectral broadening mechanism, tors (41). On the other hand, use of adjustable compensation after having done FROG mea- an ultrabroadband amplification process, and prisms in combination with chirped mirrors surements on the uncompressed continuum a dispersion compensation scheme. Self- allows for continuous adjustment of disper- (9). The duration of the resulting pulse was phase modulation is the driving force to yield sion. Using both prisms and chirped mirrors measured as 4.5 fs. For oscillators, pulses a short pulse, while the other two mecha- for dispersion compensation has the advan- with duration as short as 5.9 fs have been nisms compensate for power losses and tem- tage that the chirped mirrors only have to compensate for higher-order dispersion (i Ͼ 1 in Eq. 2). This results in a broader band- Fig. 6. Double-chirped width of the chirped coatings (38). So it is no mirror. (A) Structure surprise, that the shortest pulses to date have of a typical DCM, schematically showing been generated with a combination of mirror the path of a long- and prism dispersion compensation. Combi- wavelength beam. (B) nation of the chirped mirror and SESAM Standing-wave elec- technology should allow for dispersion com- tric field patterns in a pensation in ultracompact lasers (42). DCM structure versus wavelength. The dis- Measurement persion of the mirrors is clearly illustrated by Measurement of the extremely short pulses de- the dependence of scribed above is as much of a challenge as the penetration depth on generation itself. There is one problem inherent wavelength for the to simple autocorrelation measurements dis- range of 650 to 1050 cussed in the introduction and Fig. 2: It is nm. The highly trans- missive region around generally impossible to determine the exact 500 nm is used for shape of the pulse being measured in an auto- pumping the laser. correlation. Determination of the exact pulse width requires accurate knowledge of this shape, which is particularly difficult with the fairly complex two-cycle pulses and their strongly modulated spectra. Guessing a pulse Fig. 7. (A) Reflectivity of a typi- shape for the deconvolution of the autocorrela- cal DCM (solid line) compared to tion can give rise to inconsistent or inaccurate the gain spectrum of Ti:sapphire results. In the case of Ti:sapphire lasers, a poor- (dashed) and the measured spec- trum of a two-cycle pulse (filled ly motivated choice of an autocorrelation pulse circles). (B) Calculated phase ac- shape was shown to result in durations well cumulated after six reflections below 5 fs (6, 7). In both cases, these pulse off a DCM and a single pass durations are in contradiction to independently through a prism pair, as used in measured spectra and their respective band- the external dispersion compen- width limits. To detect such problems, the mea- sation (solid line) and phase of a two-cycle pulse, measured with surement method should also provide indepen- the SPIDER technique (filled cir- dent tests for the consistency of the data. cles). The inset in (B) shows tem- With the complex pulse shapes in the poral intensity profile of the sub–10-fs regime, techniques that allow re- pulse, determined by a Fourier trieving the pulse phase and amplitude are transform of the measured data mandatory for a proper characterization of in (A) and (B). The pulse duration is 5.9 fs. any of the sources described here. One well- established method relies on additional infor- mation from spectrally resolving the autocor- relation and is called frequency-resolved op- tical gating (FROG) (43). Another method

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poral pulse broadening. 4.4 nm range would allow for in vivo micros- Feugnet, in Advanced Solid-State Lasers, G. Dube´ and The continuous improvement of femto- copy with a good contrast between organic L. Chase, Eds. (Optical Society of America, Washing- second pulse sources has resulted in pulse compounds and water (52). In addition, a ton, DC, 1991), vol. 10, pp. 120–124; U. Keller, G. W. ’t Hooft, W. H. Knox, J. E. Cunningham, Opt. Lett. 16, durations of about two optical cycles, which spatial resolution of a few nanometers is pos- 1022 (1991). is also close to the limit given by the band- sible, comparable to electron . 26. V. Magni, G. Cerullo, S. De Silvestri, A. Monguzzi, J. width of the involved amplification and dis- The vision of new applications and attosec- Opt. Soc. Am. B 12, 476 (1995). persion compensation processes. Compres- ond science surely motivates today’s ongoing 27. H. A. Haus, J. G. Fujimoto, E. P. Ippen, IEEE J. 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We gratefully acknowl- Apart from the possible dynamic resolution, 25. F. Salin, J. Squier, M. Piche´, Opt. Lett. 16, 1674 edge financial support by the Swiss National Sci- high-harmonic x-ray radiation in the 2.3 to (1991); D. K. Negus, L. Spinelli, N. Goldblatt, G. ence Foundation.

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