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We demonstrate the transfer of a shaped spectral phase in a pulse with a sub-20-fs pulse Fourier limit of a Ti:sapphire laser to that in a deep UV pulse at 256 nm in a sum- frequency-mixing process. The generated UV pulse maintains a sufficiently broad spectrum to form a sub-20-fs pulse due to broadband sum-frequency mixing with the group-delay-dispersion-matched scheme. The spectral phases of the deep UV pulse are measured with spectral phase interferometry for direct electric field reconstruction and compared with the phase applied to the Ti:sapphire laser pulse.
©2005 Optical Society of America
1. Introduction
Spectral phase control techniques have been widely used for the generation of shaped femtosecond pulses in order to investigate ultrafast coherent interactions in physical and chemical phenomena. A highly modulated spectral phase, which cannot be given by conventional dispersive media such as a prism pair, can be used for managing the quantum states of atoms or molecules. Dudovich et al. , for example, demonstrated that a π-flipped window in the spectral phase caused a constructive interference between the upper and lower parts of the spectral component across the resonant wavelength of the intermediate state for the two-photon resonant transition of the rubidium atom, resulting in the enhanced fluorescence of the two-photon transition [1]. Another example of a sinusoidal shape of the spectral phase is essential for the application of the method of multiphoton intrapulse interference scan [2] to the selective excitation of dye molecules [3].
Most of the experiments with spectral phase control, however, have been performed in the visible (VIS) or near-infrared (NIR) region, because instruments for phase control, such as a liquid-crystal spatial light modulator (LC-SLM) [4] or an acoustooptic programmable dispersive filter (AOPDF) [5], are not transparent for other wavelength regions. Hacker et al. reported an exceptional research result at 400 nm using a micro electro mechanical system (MEMS) micromirror array [6]. It has also been reported that a state-of-the-art dispersion compensation technique with a deformable mirror yielded a pulse with a duration of 7 fs in the ultraviolet (UV) region [7, 8], and that the phase and the amplitude of the second harmonic of the Ti:sapphire laser can be controlled using an AOPDF made of fused silica in the violet~UV region[9], while the application of an arbitrarily shaped spectral phase to the broadband deep UV pulse has not been demonstrated.
Another approach to controling the phase of the UV pulse is the indirect method. This is based on the fact that the spectral phase of the broadband input pulse can be transferred, in a three-wave mixing process with a nonlinear crystal, to that of the generated pulse if the other input pulse is monochromatic, as was described in Ref. [10]. This principle is routinely applied to generate sheared replica pulses in the measurement of the spectral interferometry of direct electric field reconstruction (SPIDER) [11]. Tan et al. reported the phase control of the mid-infrared pulse by utilizing a spectral phase transfer in an optical parametric amplification (OPA) process [12], and Witte et al. also demonstrated similar results in a difference-frequency-mixing (DFM) process [13]. These experiments for femtosecond mid-infrared pulses followed the earlier work by Eickemeyer et al. observing shaped electric field transients [14]. Hacker et al. demonstrated the phase transfer in second harmonic generation (SHG) [15], and also the generation of shaped UV pulses at 200 nm in the sum-frequency mixing (SFM) process [16]. Wang and Weiner confirmed that the amplitude of a second harmonic (SH) pulse in time domain was a directly scaled version of the shaped input pulse under the type II phase matching condition [17]. The advantage of this method is that we have no need for a special device for phase control corresponding to the special wavelength.
One of the issues in the generation of the ultrashort pulse in the deep UV region, other than that of spectral phase control, is the spectral narrowing due to the large amount of group delay (GD) mismatch in the nonlinear crystal between the generated deep UV pulse and the input VIS/NIR pulses. The SFM of the fundamental pulse and SH pulse in a BBO crystal under the type I phase-matching condition, for example, caused a delay of ~ 1 ps/mm from the fundamental pulse to the generated third harmonic pulse, resulting in the acceptable spectral width of the fundamental pulse being limited to only 2.3 nm·mm [18]. In order to compensate the phase mismatch for the frequency conversion using a nonlinear crystal, the method using angular dispersion has been proposed and demonstrated [19]. Volosov et al. [20] and Martinez et al. [21] increased the phase-matching bandwidth in SHG, and Nakajima and Miyazaki investigated the effectiveness of the use of angular dispersion for third harmonic generation (THG)[22]. To achieve efficient broadband frequency conversion, Kozma et al. optimized the generation of tunable sub-30-fs UV pulses by using chirped pulses in the SFM process[23].
In this paper, we present the experimental observation of phase transfer from a sub-20-fs laser pulse of a Ti:sapphire laser to a deep UV pulse in the SFM process. The issue of spectral narrowing due to GD mismatch has been solved by adopting a novel scheme of group-delay-dispersion (GDD)-matched SFM [18], and we obtained a sufficiently broad spectrum to form a sub-20-fs pulse at 256 nm wavelength. We observed fairly good agreement between applied phases with sinusoidal and stepwise shapes in an LC-SLM in the chirped pulse amplification (CPA) system of the Ti:sapphire laser and the measured phases in the generated deep UV pulses.
2. Experiment
We have already developed a sub-20-fs CPA system of a Ti:sapphire laser with a phase controller consisting of an LC-SLM and a conventional zero-dispersion stretcher [24]. As shown in Fig. 1, we use a typical CPA system consisting of a mode-locked oscillator, an Offner stretcher, a regenerative amplifier, a four-pass amplifier, and a compressor. The phase controller with a LC-SLM is placed between the stretcher and the regenerative amplifier. In addition to the compensation of high-order dispersion in the amplified pulse from the CPA system, the additional phase modulations of sinusoidal and stepwise shapes of the pulse from this CPA system were previously demonstrated in Ref. [25].
An output pulse from the CPA system is given an appropriate chirp by adjusting the separation between the gratings of the pulse compressor so that the pulse duration of the Ti:sapphire laser should coincide with that of the quasi-monochromatic SH. The shorter edge of the spectrum is partially frequency doubled with a KDP crystal with a thickness of 8 mm in order to obtain the narrow-band quasi-monochromatic SH of sub-picosecond pulse duration due to a large GD mismatch, resulting in a wavelength of 376.5 nm with an energy of ~100 μJ. The bandwidth of 2 THz is approximately equal to the resolution of the LC-SLM [25].
The generated SH and the residual fundamental are sent to the broadband sum-frequency mixer. The details of this broadband sum-frequency mixer are described in Ref. [18]. An appropriate angular dispersion of the fundamental pulse and the noncollinear geometry of the two input pulses in this broadband frequency mixer can eliminate the limitation of the spectral width under the GD- and GDD-matching conditions, resulting in a spectral width of ~9.5 nm centered at ~256 nm with an energy of ~20 μJ. The angular dispersion of the generated UV pulse is compensated with the hybrid compensator using a prism of fused silica with an apex angle of 73° and a grating with a groove density of 1200 ℓ/mm. The angular dispersion is reduced to 3/5 with a telescope consisting of two concave mirrors with radii of curvature of 1.5 m and 2.5 m. Then the UV beam is collimated with the grating and the prism. The polarization of the UV pulse is rotated by 90 degrees with a quartz rotator, as shown in Fig. 2. These optics are configured on the basis of the results of the analysis of high-order angular dispersion described in Ref. [26].
The angular dispersion of output UV pulse from this hybrid compensator is measured by the method based on spectrally resolved interferometry proposed by Varjú et al. [27], as schematically shown in Fig. 3. Spatial fringes generated with the interferometer in Fig. 3, which cause the spatial inversion of the input pulse in one of the arms, include information on the direction of the pulse for each wavelength component, thus we can determined the angular dispersion by spectrally resolving the fringe.
The measured fringes and the angular dispersions are shown in Figs. 4 (a) and (b). The compensator with only a prism and a one-to-one telescope described in Ref. [18] exhibits the residual high-order angular dispersion, as is plotted by filled circles in Fig. 4(a), which was not resolved in the preliminary experiment [18]. The difference in angle for each wavelength component in the spectral range from 250 to 261 nm exceeds 5 mdeg. with the prism-only compensator, while it is within 1 mdeg. with the hybrid compensator of the prism and the grating, as is shown in Fig. 4(b). Due to the large Fresnel loss of the prism and the low diffraction efficiency (~60 %) of the Al-coated grating, the pulse energy is estimated to be a few μJ at the output of the hybrid compensator.
Fig. 3. Schematic of the interferometer for the measurement of the angular dispersion. Vertical fringes generated with this interferometer are spectrally resolved with a slit and a grating with a groove density of 2400 ℓ/mm and detected by a CCD camera.
Fig. 4. Upper parts of both figures are the spectrally resolved figures for the measurement of the angular dispersion. (a) With the prism-only compensator. (b) With the hybrid compensator. Relative angles for the propagation directions in each spectral component resulting from these fringes are shown as filled circles in both figures. Solid curves are obtained from the ray-trace calculation described in ref. [26].
The pulse duration of the generated UV was expected to be a few ps due to the dispersions suffered from the extention of the grating separation in the CPA system, from the angular disperser in the broadband frequency mixer, and from the hybrid angular dispersion compensator. Thus, we measured the GDD in the generated deep UV pulse by the cross-correlation spectrally and temporally resolved down-conversion technique instead of the upconversion technique (STRUT) proposed by Rhee et al. [28], before utilizing the SPIDER apparatus. Note that the measured pulse duration with the SPIDER should be shorter than the delay between the two replica pulses needed for the SPIDER measurement.
Approximately half of the energy of the fundamental pulse was sent to a ”recompressor”, which consists of a pair of gratings with a groove density of 150 ℓ/mm to compensate for the positive chirp given in the compressor in the CPA system, and then difference-frequency-mixed with the deep UV pulse. The spectrum of the generated DFM pulse was recorded at each delay between the fundamental and the deep UV pulse. We found that the duration of the deep UV pulse is ~3 ps and determined that the GDD and the third-order dispersion (TOD) are 8.2×10-27 [s2] and 2.4×10-41 [s3], respectively, from the measured spectrogram shown in Fig. 5. A pair of prisms made of fused silica with a separation of 41.5 cm was utilized for removing most of the GDD. We obtained a pulse duration of 170 fs by adjusting the insertion of the prism pair such that the measured duration of the cross-correlation trace could be minimized.
The phase of the deep UV pulse behind the prism pair was measured with the SPIDER apparatus (Fig. 6). We used a Michelson interferometer to generate a pair of replicas of the UV pulse with a fixed delay of 1.227 ps. Two beam splitters, having the same thickness, generate two replicas of the UV pulse, resulting in the dispersions due to the transmission in these two beam splitters being the same. The zero-additional-phase (ZAP) SPIDER [29]does not need such an interferometer for the measured UV pulse. We did not, however, adopt the ZAP-SPIDER because the collinear geometry of the interferometer generates spectral fringes without adjusting the size of the beam waist on the slit of the spectrometer, and the energy of the UV pulse is sufficiently high to generate the difference-frequency-mixed pulse behind the interferometer.
A pair of gratings with a groove density of 1200 ℓ/mm was used to generate a chirped NIR pulse from a portion of the fundamental pulse. Two replicas of the deep UV pulses were difference-frequency-mixed with the chirped NIR pulse in a BBO crystal with a thickness of 20 μm. The generated two pulses were spectrally sheared by 2 THz due to the high chirp of the NIR pulse and the delay between the replicas of the UV pulse. This pair of spectrally sheared and temporally delayed pulses was sent to a spectrometer (Ocean Optics Inc., HR2000), and the spectral interferogram was recorded. We extracted the information of the spectral phase with the inverse Fourier transform of this interferogram.
The GDD given by the grating pair in the SPIDER apparatus is -1.1×10-25 [s2], which is approximately ten times larger than that due to phase control with the LC-SLM (9×10-27 [s2]), so that the change of the spectral shear of the two replica pulses with phase control can be estimated to be ~ 10 % at most. Greater GDD of the grating pair would reduce this type of error.
The measured phase without phase control of the LC-SLM reveals an unexpected phase distortion (Fig. 7(a)) which might be caused by the roughness of the surface of the concave mirrors used in the broadband frequency mixer and the hybrid compensator. This type of phase distortion induced by a stretcher for a CPA system was analyzed and measured by Bagnoud and Salin [30]. The Fourier transform of the measured spectrum and the phase with the distortion exhibits a modulated temporal profile over a ~170 fs duration, as shown in the inset of Fig. 7(a), which is consistent with the duration indicated by the cross-correlation measurement.
Fig. 7. Measured interferograms (hatched areas) and spectral phases (solid curves). The measured phases (a) without phase control and (b) with the inverse of the phase distortion applied. Applied phases (dashed curves) are given by the equations (c) ϕ =cos{2π(ν - ν 0)/∆ν} and (d) ϕ =tanh{(ν - ν′0)/∆ν′}, where ν 0=800THz, ∆v=10THz, ν′0=805THz, and ∆ν′=1THz. Temporal profiles calculated from the spectrum and the measured/applied phases are also shown as solid/dashed curves in the insets.
We applied the inverse of the phase distortion to the LC-SLM to cancel out the phase distortion, resulting in most of the distortion being eliminated (Fig. 7(b)), while the residual phase distortion adds subpeaks in the temporal profile to the main peak of the pulse with a duration of 20 fs, which is 11% longer than that of 18 fs calculated from the Fourier limit of the measured spectrum. The residual phase distortion may be due to the unexpected nonlinear effect in the SFM process, such as the cross phase modulation in the BBO crystal.
Because of the elimination of the phase distortion, we can expect further phase transfer from the fundamental pulse to the generated UV pulse by adding the shaped spectral phase to the inverse of the phase distortion. The results of the measured phases for a sinusoidal shape and a stepwise shape are shown as solid curves in Figs. 7(c) and (d), respectively. The dashed curves in these figures correspond to the applied phases. Although there are residual phase distortions in the measured phases, we can see fairly good agreement between the measured phases and the applied phases in both figures. Note that the addition of the spectral phase to the fundamental pulse has an influence on the power spectrum of the generated UV pulse. The interferograms with the SPIDER measurement, shown as hatched areas in Figs. 7(c) and (d), reflect the modulated intensity of the power spectrum. The phase-matching conditions in the SFM process might be slightly changed by the spectral phase control.
3. Summary
We demonstrated the transfer of the shaped spectral phase in a sub-20-fs pulse of a Ti:sapphire laser to that in a deep UV pulse at 256 nm. By indirect phase control via the SFM process, the spectral phases in the deep UV pulses are controlled by applying phase modulation to the LC-SLM in the CPA system. However, the correspondence between the applied and transferred phases should be improved to enable the practical application of these pulses.
This work was supported by the Ministry of Education, Culture, Sports, Science, and Technology (MEXT) through a Grant-in-Aid for Scientific Research for Young Scientists (A) No.16686006.
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