Mirrorless single-shot tilted-pulse-front autocorrelator

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1 Figueira et al. Vol. 22, No. 12/ December 2005 / J. Opt. Soc. Am. B 2709 Mirrorless single-shot tilted-pulse-front autocorrelator Gonçalo Figueira, Luís Cardoso, Nelson Lopes, and João Wemans GoLP/Centro de Física dos Plasmas, Instituto Superior Técnico, Avenida Rovisco Pais , Lisbon, Portugal Received January 4, 2005; revised manuscript received May 17, 2005; accepted June 17, 2005 Ultrashort pulses exhibiting angular dispersion have their pulse front tilted relative to the phase front. This leads to a serious degradation in the focused peak power, making the use of adequate diagnostics indispensable. Here we present an upgrade to a previously demonstrated uniaxial single-shot autocorrelator for ultrashort laser pulse-width measurements that extends its versatility, by making it suitable for detecting and correcting tilted pulse fronts. We have used this diagnostic to optimize the alignment of our chirped-pulseamplification grating compressor Optical Society of America OCIS codes: , , , , INTRODUCTION The concept of chirped pulse amplification 1 (CPA) presently dominates the high-peak-power laser technology scenario, with many facilities worldwide operating or developing ultrahigh-intensity laser chains capable of attaining power levels from the terawatt W to the petawatt W scale. This is achieved by generating moderate-to high-energy pulses with durations varying from a few tens to a few hundreds of femtoseconds. The CPA mechanism starts with a short fs, low-energy nanojoules laser pulse, which is then expanded in time by several orders of magnitude, typically up to the nanosecond level, with the purpose of decreasing the instantaneous intensity during amplification and propagation through the laser chain. The pulse is then amplified and finally compressed to a duration that is ultimately defined by the available spectral bandwidth at the output and the amount of spatial and spectral distortions introduced. One achieves pulse-width expansion and compression by applying a controllable, reversible dispersion (chirp) to the spectral content of the pulse, which is normally achieved by means of conjugate diffraction grating pairs: a positive dispersion one acting as a pulse stretcher (antiparallel grating pair with an intermediate unit-magnification optical system) and a negative dispersion one as the compressor (parallel grating pair). A proper alignment of the grating compressor is therefore one of the most crucial requirements of a CPA laser 2 if one wants to obtain the highest possible peak powers. For instance, a slight deviation from perfect parallelism between the gratings will generate an inhomogenous compressed pulse, exhibiting an angular frequency chirp across its aperture and an angular dispersion. As shown in Fig. 1, such a pulse will have its pulse front tilted with respect to the direction of propagation, whereas its phase front will be orthogonal to it. 3 In general, 4 the relation between the tilt angle and the angular dispersion is tan = d d, 1 where is the wavelength and is the dispersion angle. Although locally such a pulse may have a short duration, on focusing, a tilted pulse front will result in a spread of energy both in space and in time relative to an untilted one and, consequently, in a considerable decrease in the expected focused intensity. The resulting increase in pulse duration due to pulse-front tilt alone is given by 5 = D c tan = D d c d, 2 where D is the beam diameter before focusing and c is the speed of light. In the particular case of a grating compressor with a single-pass angular error of x in the dispersion plane, 2,3 we have = D c 2N tan d x, 3 cos i where i and d are the incidence and diffracted angles, respectively, and N is the grating groove parameter. For instance, taking the parameters i =72.0, d =61.8, and N=1740 lines/mm, one finds that an angular error of x =100 rad will result in an angular dispersion of 2.1 rad/nm; a beam of =1053 nm, D=3 cm will acquire a front tilt angle of 2.2 mrad, resulting in an increase of 220 fs in its focused duration, which is unacceptable in the short-pulse regime. Therefore, in CPA lasers it is particularly essential to use a pulse-front tilt monitoring and correcting diagnostic, since the near-field pulse duration may differ significantly from the focused one. Several methods for diagnosing and eliminating tilted pulse fronts have been proposed and demonstrated, such as interferometric field autocorrelation, 3 single-shot autocorrelation of flipped replicas of the pulse [or tilted-pulsefront single-shot autocorrelation 6,7 (TPF-SSAC)], spec /05/ /$ Optical Society of America

2 2710 J. Opt. Soc. Am. B/ Vol. 22, No. 12/ December 2005 Figueira et al. Fig. 1. Geometry of a tilted pulse front. The phase fronts, corresponding to the vertical lines, are perpendicular to the propagation direction, with the pulse front tilted by an angle. 0 is the central wavelength, d =d is the angular dispersion, and D is the beam diameter. trally resolved interferometry, 8 and grating-eliminated no-nonsense observation of ultrafast incident laser light E fields (GRENOUILLE). 9 Of these, TPF-SSAC is the only one that allows correction of the tilted pulse front and measurement and optimization of the pulse duration in real time, in a visually straightforward manner and without requiring additional processing. Given the secondharmonic-generation process involved in the autocorrelation principle, it does require enough intensity to work, which makes it especially adequate for characterizing high-power laser chains. In this paper, we demonstrate that, by applying a small modification to the design of a previously proposed uniaxial single-shot autocorrelator, it becomes a TPF- SSAC while retaining the uniaxial nature. Moreover, it can be used to detect the tilted pulse front and perform pulse autocorrelation along any arbitrary direction. Once the tilt has been corrected, one can quickly revert it to the original single-shot autocorrelator setup. All these operations require no alignment of the incoming beam. 2. TILTED-PULSE-FRONT SINGLE-SHOT AUTOCORRELATION In a single-shot autocorrelator, 10 the temporal profile of the pulse is imaged into the spatial domain, by one s making two replicas of the pulse to be characterized interact at an angle inside a nonlinear crystal. In the region where the two replicas overlap spatially and temporally, a sumfrequency-generated signal is emitted, parallel to the bisector of the crossing angle. Given the interaction angle, each transverse coordinate of this signal in the interaction plane corresponds to a fixed delay between the two pulses. The relation between the full width at halfmaximum (FWHM) of the resulting spatial shape x and that of the initial pulse duration t is given by 11 of a beam splitter. To direct the pulses to the crystal with the adequate interaction angle and to provide equal delay to each arm of the autocorrelator, several additional mirrors are required, as well as an adjustable delay line. Also, the beam splitter will flip the reflected pulse front relatively to the splitting plane, as will each reflective surface on its reflecting plane. The relative flipping of the two replicas when they meet in the crystal is therefore defined by the total number and orientation of the reflecting surfaces between the beam splitter and the crystal. In the case in which no pulse-front tilt is present, the autocorrelation trace is independent of the number or mirrors. However, in the general case in which a pulse-front tilt may be present in both the horizontal x and the vertical y directions, the measured autocorrelation width and position will depend on whether the flipping is present or not, since the tilt will cause both the relative interaction angle and the overlapping delay to vary. These effects are illustrated in Fig. 2, where a single-shot autocorrelation setup with tilted pulses is shown. Note that in the figure we have labeled the crossing angle of the propagation vectors outside the crystal as 2, corresponding to 2 inside the crystal. In this example, the pulse fronts have a tilt in the horizontal x z plane. In the top figure, the pulse fronts have been relatively flipped, resulting in an effectively increased interaction angle inside the nonlinear crystal, which narrows the autocorrelation trace. In the bottom figure, the same pulse fronts are shown, without relative flipping. In this case, although the interaction angle inside the crystal and the resulting autocorrelation width are unaffected (relative to the untilted pulse conditions), yielding a correct duration measurement, 7 the autocorrelation trace will be spatially displaced because both the interaction position and the bisector angle orientation have changed. The principle of the TPF-SSAC is to decouple the measurements of the autocorrelation shape and the amount of pulse-front tilt: One of the replicas is flipped in both planes, and the tilt is detected in each direction at a time by correlating the replicas in the orthogonal direction. In this fashion, the presence of a tilt will result in an oblique autocorrelation, whose inclination is given by 6 2n sin t = K x, 4 c where K is a factor relating a given pulse-shape width to that of its autocorrelation, n is the refractive index of the nonlinear crystal, and is half the crossing angle inside it. In traditional autocorrelator designs, the two pulse replicas are obtained through amplitude division, by means Fig. 2. Influence of a tilted pulse front on the autocorrelation trace. (a) Two pulse fronts with a tilt in the x z plane, relatively flipped, resulting in a shorter autocorrelation. (b) The same pulse fronts without flipping, resulting in a displaced autocorrelation trace (the dotted autocorrelation trace corresponds to that above for comparison).

3 Figueira et al. Vol. 22, No. 12/December 2005 / J. Opt. Soc. Am. B 2711 Fig. 3. Tilted-pulse-front single-shot autocorrelator. (a) Setup when viewed from the top. Each of the pulse fronts A and B shown has a tilt in the plane orthogonal to the x z plane that contains its propagation direction, and they are relatively flipped about the x z plane. This is illustrated by means of using a solid (dotted) line to mark the uppermost (lowermost) position of each pulse front. (b) Same setup when viewed from the side, for greater visual clarity. x sin cos + y =0, where is the interaction angle inside the nonlinear crystal and and are the tilts in the horizontal and vertical planes respectively. A corresponding, simplified interaction setup is illustrated in Fig. 3. Two pulse replicas A and B interact inside a nonlinear crystal. Each of the pulse fronts has a tilt in the plane orthogonal to the x z plane that contains its propagation direction (i.e., its local vertical plane). In the top figure, representing the top view of the setup, this is illustrated by using a solid line to indicate the position of the pulse front at the uppermost y coordinate of the beam aperture and a dotted line for the lowermost one. The bottom figure, corresponding to the side view, shows the relative pulse-front orientation from this perspective. For the sake of clearness, the tilts in the x z plane have been omitted from the figure. Inside the crystal, we have also represented the same lines, and, from their overlapping points, it becomes clear that each y coordinate of the beam will have its autocorrelation imaged at a different x coordinate on the CCD camera screen. With mirrors, a minimum of seven surfaces is needed to provide and maintain the flip in both directions and to adjust the relative delay and the interaction angle. Additionally, changing from horizontal to vertical autocorrelations and vice-versa, requires realigning several of these mirrors, in a noncoplanar setup. All these degrees of freedom can make the TPF-SSAC setup complicated to work with. 3. DESCRIPTION The setup proposed here eliminates all the complications inherent to the multimirror, noncoplanar nature of the described setup. It consists in a small modification to a uniaxial design originally introduced by Collier et al. 12 and is shown in Fig. 4. Instead of a beam splitter, the pulse is divided by means of a Wollaston prism, a polarizing element that angularly separates the beam into two orthogonal polarization components. A half-wave plate is used to balance the amount of energy in each arm. One can make the two beams overlap inside the crystal with 5 the appropriate angle by refracting them in a biprism or a second Wollaston prism with an adequate wedge angle. The nonlinear crystal is cut for optimum type II sumfrequency generation for the wavelengths involved. The autocorrelation signal emerges in the same direction as the original incoming beam and is imaged onto a CCD detector by an objective lens. A diaphragm is used to block spurious self-generated second-harmonic signals, and a bandpass filter at the CCD entrance removes any residual fundamental radiation. In this most elementary configuration, the device will already be capable of producing autocorrelation traces. The original design features additional elements such as a cylindrical lens to increase the intensity in the crystal in the direction orthogonal to the autocorrelation and an optional, ingenious method of extending the measurement range to longer durations, consisting of previously imposing a calibrated front tilt on the pulse to be characterized by means of a diffraction grating and then flipping one of the replicas along the same direction as the autocorrelation, so that the crossing angle of both pulse fronts inside the crystal will increase. The flipping is done recurring to a Dove prism, which reverses left and right without changing the propagation direction; optical compensation for the other arm is ensured by a glass block with the same optical path. Our modification consisted in recognizing that a second, orthogonal Dove prism could be used instead of the glass block, to provide vertical flipping, and thereby convert this autocorrelator into a TPF-SSAC. In this fashion, each Dove prism acts as a pair of mirrors, but the setup remains coplanar and uniaxial in nature. In fact, one can rapidly switch between the elementary and the TPF- SSAC setups just by inserting the two orthogonal prisms (and removing the cylindrical lens, if used) without needing to realign the input beam or any of the other optical elements. Moreover, and given the compact footprint of this autocorrelator, one can quickly switch between characterizing the horizontal and the vertical pulse-front tilts either by rotating the whole device (ours is assembled on a single 30 cm slide) or, alternately, by assembling each prism (Wollaston, Dove pair, and biprism) in a rotating mount centered on the propagation axis, again with no need for realignment. 4. ANALYSIS It may be argued against this design that the introduction of prisms, being dispersive elements, may affect the pulse-front tilt characterization, since they will introduce an angular dispersion themselves and will enlarge the pulse duration. A careful analysis must therefore be performed to understand the role and influence of this instrument-induced tilt. The influence of the dispersive optics may originate two types of measurement error: (i) Fig. 4. Autocorrelator setup. /2, half-wave plate; WP, Wollaston prism; DP1 and DP2, Dove prisms; BP, biprism; NC, nonlinear crystal; L, imaging lens; CCD, camera.

4 2712 J. Opt. Soc. Am. B/ Vol. 22, No. 12/ December 2005 Figueira et al. masking of the original angular dispersion and (ii) changing the pulse autocorrelation width. The first type of error is originated by addition of angular dispersion in the plane orthogonal to that of the autocorrelation. By analyzing Fig. 4, we may notice that such type of dispersion could be introduced only during propagation inside the vertical-flipping Dove prism DP1. Given that this prism is optically equivalent to a slab of glass with parallel faces, all the wavelengths emerge from it with the same angle, and the measurement is not affected. The second kind of error is linked to the autocorrelation plane and may have two origins: (i) The induced tilt in the horizontal direction may cause the pulse fronts to overlap inside the crystal at an erroneous angle, thus producing a misleading autocorrelation, or (ii) the longitudinal material dispersion may increase the actual pulse duration. As for the first effect, we start by examining the mechanism through which the pulses are split at the Wollaston prism, which is linked to the geometry and composition of the prism. This prism is formed by two blocks of calcite united at a plane that is oblique to the propagation direction at an angle. The blocks are oriented such that their optical axes are orthogonal to each other and to the propagation axis; this leads to a switching of roles between the ordinary and the extraordinary rays when the beam propagates from the first block into the second block. Furthermore, since this interface is at an angle, the different changes in the refractive index for each ray will cause them to separate in an approximately symmetrical fashion around the input beam direction, with angles given by sin e = sin n o cos ne 2 n o 2 sin 2, sin o = sin n e cos no 2 n e 2 sin 2, where is the output angle from the prism, n n is the refractive index, and the subscripts o, e stand for ordinary and extraordinary, respectively. From this, one can show that the angular dispersion (and, consequently, the tilt) for both emerging beams is also symmetrical around the input axis. The influence of the biprism is also clearly symmetrical for both beams and can be accounted for by using the well-known formulas for dispersive propagation inside prisms. 13 The symmetry is broken by the horizontal Dove prism DP2, which flips both the added tilt (thus cancelling the effect of the other arm) and the original tilt [the in Eq. (5)], such that the device becomes a true TPF-SSAC. The canceling is not complete, but in our case it corresponds to a residual angular dispersion of rad/nm over the wavelength range m. These results are shown in detail in Table 1 for operation at 1053 and 800 nm. The values indicated under each of Table 1. Pulse-Front Tilt (in mrad) after Dispersive Elements (nm) Wollaston Dove Biprism 1053 Ordinary Extraordinary Ordinary Extraordinary the three prisms correspond to the accumulated instrument-induced pulse-front tilt in millirads, for both the ordinary and the extraordinary beams. In this case, the extraordinary beam is laterally flipped in the Dove prism, acquiring an opposite pulse-front tilt. As can be seen, for both wavelengths the two beams emerge from the biprism with approximately the same tilt, corresponding to interaction without relative flipping. As discussed above, in this case the autocorrelator will provide a correct measurement of the pulse duration. The residual difference = o e in the tilt angle, shown in the last column, is such that (with rad) and therefore has no influence on the autocorrelation trace, even for ultrabroadband 100 nm pulses. Finally, we will calculate the pulse duration enlargement due to the dispersion introduced by each element. Fora1/e in amplitude input pulse duration 0, the output pulse duration f is given by f = k 2 0 L, 7 where k 0 =d 2 k/d 2 is the second derivative of the wavenumber k evaluated at the central frequency, is the frequency, and L is the length of material traversed. Introducing the adequate values from the refractive indices and material lengths (Wollaston prism: calcite, 10 mm; biprism and Dove prisms: BK7, 25 mm), we find that a pulse of 0 =100 fs at 1053 nm would be enlarged by 0.8 fs and a pulse of 0 =50 fs would be enlarged by 5.8 fs. This is perfectly acceptable in this duration range, provided that this enlargement is taken into account, and is ultimately the limiting feature in this instrument s performance. However, at 800 nm the dispersion becomes more severe, and the corresponding broadened pulse widths would be and 68 fs. Given the versatile nature of this instrument, a possible solution to attenuate this effect would be to achieve the pulse-front tilt correction first and then simply remove both Dove prisms to perform the autocorrelation measurement, which would eliminate about 20 mm of optical glass. In any case, the presence of the remaining dispersive elements limits the optimum working range of this setup to pulse widths above 50 fs. Regarding the minimum detectable pulse-front tilt, it is ultimately defined by the resolution available with the imaging system and CCD sensor. The problem is equivalent to that of detecting the minimum displacement x in two autocorrelation curves separated by the vertical width y of the CCD sensor, such that, from Eq. (5) and in the absence of horizontal tilt, the minimum detectable tilt in the vertical plane is given by min = x sin / y. By adjusting two Gaussian curves to each autocorrelation curve and determining their centroids, it is possible to achieve subpixel resolution, but we may use an estimate of x=1 pixel. Given that, for our CCD, y=400 pixels and 0.1, we obtain min 0.25 mrad. At 1053 nm, this corresponds to a minimum detectable angular dispersion of 0.24 rad/nm, which is comparable with that of other dedicated instruments. 5,8,9 5. MEASUREMENTS We have used this modificated TPF-SSAC to optimize the alignment of the grating compressor of our terawatt CPA 0 2

5 Figueira et al. Vol. 22, No. 12/ December 2005 / J. Opt. Soc. Am. B 2713 Fig. 5. front. Vertical autocorrelation trace denoting an untilted pulse Fig. 6. Autocorrelation trace of a compressed pulse exhibiting a tilted front. The upper trace is a time-delayed replica caused by an internal reflection in the device. Fig. 7. Temporal profile of the autocorrelation for pulses with tilted and untilted pulse fronts. laser chain. 14 The seed pulses are generated by a Coherent Mira pumped by a 10 W Verdi, having a duration of 100 fs and a FWHM bandwidth of 14 nm centered at 1053 nm. These pulses are then stretched to 0.9 ns by a pair of 1740 lines/ mm diffraction gratings whose effective optical separation is 1200 mm, with an Offner triplet designed to pass 40 nm as the imaging optical system. The pulses are then amplified to 3 mj in a second-harmonic Nd: YAG-pumped, Ti:sapphire regenerative amplifier, at a 10 Hz repetition rate. Further amplification to the joule level is achieved by our double passing a 16 mm diameter Nd:phosphate rod amplifier; for the purpose of aligning the compressor, we just double pass the rod without amplification, in order to maintain the repetition rate but still include the additional material dispersion introduced by this amplifier. After a vacuum spatial filter, the pulses are sent to the grating compressor, housed inside a vacuum chamber. The compressor is aligned at atmospheric pressure, and, once in vacuum, the optical path between the gratings will change slightly owing to the variation of the refractive index of air with pressure; to compensate for this, we have equipped the stretcher grating mount with a translation stage. The compressor is arranged in a double-pass configuration, with a grating separation around 600 mm. This means that not only the input beam angle and the grating parallelism must be accurately adjusted but also that the returning mirror pair must maintain the incidence and diffracted angles for the second pass. We found that initially there was a small pulse-front tilt present in our compressed pulse, which was easy to correct with the aid of this diagnostic. For that, we adjusted the angles of incidence on the second grating and the returning mirror pair, by means of micrometer actuators that were dimensioned to provide a rotation of 2.8 mrad per turn. The resulting autocorrelation trace is shown in Fig. 5. To illustrate the capability of the device, we have also acquired a trace of the autocorrelation for a large front tilt, introduced by deliberately deviating the grating pair from parallelism and correcting for the resulting change in their separation in order to obtain the shortest autocorrelation. The result is shown in Fig. 6. The double trace is caused by an internal reflection in the device that appears delayed in time and is not a physical feature of the pulse; it can be removed by suitable spatial filtering for the tilt-corrected autocorrelation. From the image, we can appreciate that the actual trace width at any height does not change significantly from the corrected version of Fig. 5, as evidenced by the corresponding temporal profiles in Fig. 7, which illustrates the necessity of using this kind of autocorrelator. 6. CONCLUSION The presence of undetected tilted pulse fronts was seen to play an important part in degrading the performance of CPA laser systems. The TPF-SSAC emerges as a compact, double-purpose device capable of diagnosing this effect and simultaneously providing information about the pulse duration, in an immediately understandable fashion. This is especially useful for the real-time alignment of CPA grating compressors. The uniaxial TPF-SSAC introduced here is simple and straightforward to align. It can be quickly readjusted to provide tilt and autocorrelation measurements in either the horizontal or vertical axis, with no need for realigning the incoming beam or any other external optics. The fact that dispersive optics are used in the device was shown to be acceptable. Experimental measurements of a compressed CPA pulse confirm this behavior. These features, together with its compact footprint, make it an extremely versatile and useful instrument. ACKNOWLEDGMENT This work was supported by Fundação para a Ciência e a Tecnologia under grant POCTI/FAT/41586/2001. Corre-

6 2714 J. Opt. Soc. Am. B/ Vol. 22, No. 12/ December 2005 Figueira et al. sponding author G. Figueira can be reached by at REFERENCES 1. D. Strickland and G. Mourou, Compression of amplified chirped optical pulses, Opt. Commun. 56, (1985). 2. C. Fiorini, C. Sauteret, C. Rouyer, N. Blanchot, S. Seznec, and A. Migus, Temporal aberrations due to misalignments of a stretcher-compressor system and compensation, IEEE J. Quantum Electron. 30, (1994). 3. G. Pretzler, A. Kasper, and K. J. White, Angular chirp and tilted light pulses in CPA lasers, Appl. Phys. B 70, 1 9 (2000). 4. J. Hebling, Derivation of the pulse front tilt caused by angular dispersion, Opt. Quantum Electron. 28, (1996). 5. K. Osvay, A. P. Kovacs, Z. Heiner, G. Kurdi, J. Klebniczki, and M. Csatari, Angular dispersion and temporal change of femtosecond pulses from misaligned pulse compressors, IEEE J. Sel. Top. Quantum Electron. 10, (2004). 6. Z. Sacks, G. Mourou, and R. Danielius, Adjusting pulsefront tilt and pulse duration by use of a single-shot autocorrelator, Opt. Lett. 26, (2001). 7. M. Raghuramaiah, A. K. Sharma, P. A. Naik, and P. D. Gupta, Simultaneous measurement of pulse front tilt and pulse duration of a femtosecond laser beam, Opt. Commun. 223, (2003). 8. K. Varjú, A. P. Kovács, G. Kurdi, and K. Osvay, Highprecision measurement of angular dispersion in a CPA laser, Appl. Phys. B 74, S259 S263 (2002). 9. S. Akturk, M. Kimmel, P. O Shea, and R. Trebino, Measuring pulse-front tilt in ultrashort pulses using GRENOUILLE, Opt. Express 11, (2003). 10. J. Janszky, G. Corradi, and R. N. Gyuzalian, On a possibility of analysing the temporal characteristics of short light pulses, Opt. Commun. 23, (1977). 11. F. Salin, P. Georges, G. Roger, and A. Brun, Single-shot measurement of a 52-fs pulse, Appl. Opt. 26, (1987). 12. J. Collier, C. Danson, C. Johnson, and C. Mistry, Uniaxial single shot autocorrelator, Rev. Sci. Instrum. 70, (1999). 13. E. Hecht, Optics, 3rd ed. (Addison Wesley Longman, 1998). 14. G. Figueira, N. Lopes, L. Cardoso, J. Wemans, J. M. Dias, M. Fajardo, C. Leitão, and J. T. Mendonça, Performance and characterization of a 2.8 TW Ti:sapphire-Nd:glass chirped pulse amplification laser system, in XV International Symposium on Gas Flow, Chemical Lasers, and High-Power Lasers, J. Kody Mora, ed., Proc. SPIE 5777, (2005).

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