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A novel method for compressing a laser pulse, using a combination of transient stimulated Raman scattering and a pump-probe technique, is proposed. The approach does not require a short laser pulse, in contrast to a reported method based on impulsive stimulated Raman scattering. The observed spectrum was sufficiently broad to generate a sub-10 fs pulse. In fact, a 100-fs pulse in the near-ultraviolet region was compressed to the sub-30 fs. Further compression of the laser pulse would be achieved by compensating for phase distortion, as suggested from the observed data of the spectral phase.
©2006 Optical Society of America
1. Introduction
A femtosecond laser has been developed and has been successfully utilized in a variety of applications, including studies of ultrafast phenomena. It has recently been reported that even a laser with a pulse duration of a few optical cycles can be directly generated from a Ti:sapphire laser oscillator [1] and is available on the market from several manufacturers. A high-energy few-cycle pulse can be generated by expanding the spectral domain of the femtosecond pulse amplified in a regenerative [2] or multi-pass amplifier [3]. For instance, generation of few-cycle pulses using broad-band second harmonic generation [4] or self-phase modulation [5] are reported. This type of technique is based on frequency modulation of the laser pulse through a nonlinear optical effect and subsequent phase control of the wide-range spectral components.
The frequency modulation is also achieved using Raman-type nonlinear optical phenomena. A broad spectrum extending from the deep-ultraviolet to the near-infrared is produced by two-color stimulated Raman scattering (SRS) [6,7]. In this technique, a two-color nanosecond laser, the frequency separation of which is adjusted to the Raman shift frequency, is used for SRS and subsequent four-wave Raman mixing (FWRM) to give a spectrum consisting of numerous Raman sidebands. A broad spectrum is also obtained by transient SRS using a single-color picosecond laser [8]. Shverdin et al. recently reported on the generation of a train of periodic 1.6-fs pulses with an 11-fs interval using a two-color nanosecond laser, the frequency separation of which is slightly detuned from the Raman shift frequency [9]. The generation of a single optical pulse rather than a train of periodic pulses is, however, difficult using the nanosecond and picosecond lasers that are mentioned above.
An alternate Raman-based pulse compression technique based on a combination of impulsive SRS [10] and a two-color pump-probe technique is also available [11–15]. This approach has the potential for generating an ultrashort single optical pulse rather than periodic pulses [13–15]. This technique has already been demonstrated in the ultraviolet region by Noack et al. [15] and can even be used in the deep-ultraviolet region. When a single-color femtosecond laser is used for the generation of Raman emissions, self-phase modulation which is caused at high laser intensity, becomes conspicuous and hence the efficiency in transient SRS is substantially decreased [8]. In the two-color pump-probe technique, self-phase modulation is, however, minimal and does not affect the spectral shape of the probe pulse, and hence, improves efficiency in the generation of Raman emission [11]. This useful technique, however, requires a very short pump pulse to induce impulsive SRS for the phase modulation of the subsequent delayed probe pulse. For example, a pump pulse shorter than 30 fs is employed for the excitation of coherent rotational motion of a hydrogen molecule [12].
In this report, a novel compression technique based on transient SRS and a pump-probe technique is proposed. Similar to the above approach, the two-color pump-probe technique is utilized to reduce undesirable self-phase modulation. Instead of impulsive SRS, transient SRS was used for the excitation of coherent molecular motion, which allows the use of a relatively long pump pulse. In this study, we utilized a pump pulse in excess of 100 fs, which is appreciably longer than the rotational period of a hydrogen molecule. The combination of transient SRS and the pump-probe technique has long been used to observe the dephasing process of coherent molecular vibrations [16]. The mechanism of coherent scattering is discussed in detail in Ref 17.
In comparison with impulsive SRS, a major disadvantage of transient SRS may be a low efficiency for the generation of Raman emission, since an intense pump pulse is needed to exceed the threshold. This is in contrast to the case of impulsive SRS, which is achieved using an intense ultrashort pump pulse with a broad spectrum [10]. The intensities of the Raman sidebands obtained in this study were, however, sufficient for the generation of sub-10-fs pulses (see below). A distinct advantage of this method is its use of a conventional 100-fs Ti:sapphire laser, since a laser producing a pulse shorter than 30 fs is more complicated and is also expensive.
2. Important ractors in coherent Raman scattering
When an intense laser pulse propagates in a transparent medium, a nonlinear polarization is induced as the result of the interaction between the pulse and the medium. This behavior can be described by the following equation:
where Δ is Laplacian, n is the refractive index of the medium, E is the electric field of the laser beam, and P NL is the nonlinear polarization induced in the medium. If the medium is Raman active and the pulse width of the laser beam (hereafter denoted by the pump beam/pulse) is shorter than the dephasing time, the coherent motion <q> of the medium is induced as a result of transient SRS [17]:
where k v is the wave vector of coherent motion with angular frequency ω v, Q(r, t) is the amplitude of coherent motion, and c.c. is abbreviation of the complex conjugate. The amplitude <q> reaches a maximum immediately after the propagation of the pump beam, and then decreases through a dephasing process [17]. If a relatively weak pulse (hereafter denoted by probe beam/pulse, electric field E probe, wave vector k probe, and angular frequency ω probe) is passed through the medium after a certain time delay t D from the pump pulse, coherent scattering, which is depicted by the following polarization P NL, is generated, provided that the time delay is less than the dephasing time:
where N is the number density of the molecule, and (∂α/∂q)0 is the derivative of the polarizability with respect to the coordinate q. As the result of this interaction, additional frequency components, i.e.,ω S = ω probe - ω v and ω A = ω probe + ω v, which are referred to as Stokes and anti-Stokes components and propagate with wave vectors k S and k A, respectively, are generated. For both the components, the intensity I A,S(t D) after the interaction along the distance l is obtained by solving Eq. (1)-(3) [17];
where the phase mismatch Δk A,S is (k probe-k s-k v)· r̂ and (k A-k probe-k v)· r̂ for the Stokes and anti-Stokes components, respectively, n A,S indicates the refractive index of the medium at the wavelength of the Raman emission, and r̂ is the unit vector, the direction of which is identical to that for beam propagation. The intensities of the Stokes and anti-Stokes components achieve maximum values under phase matching conditions (Δk A,S = 0) and decrease with an increase in the degree of phase mismatch. This phase mismatch is usually caused by the dispersion of the medium (change in refractive index against wavelength), which is known to be smaller in gases than in condensed media such as liquids or solids. High-order Stokes and anti-Stokes components are also generated through this coherent scattering process. One of the important features of the Raman scattering is that the intensity of the Stokes emission for the n-th order is nearly equal to that of the anti-Stokes emission for the n-th order, when the pump and probe beams propagate collinearly and the pulse width of the probe beam is longer than the period of coherent molecular motion [17]. Thus, a symmetrically shaped spectrum would be expected. Another remarkable feature is that the efficiency for the conversion from the probe pulse to the Raman sidebands does not depend on the intensity of the probe pulse. However, if the energy of the probe pulse is sufficiently high to induce a transient SRS or the pulse duration is sufficiently short to induce impulsive SRS, the scattering efficiency may be dependent on the intensity of the probe pulse, leading to an unsymmetrically shaped spectrum consisting of Stokes and anti-Stokes emissions with different intensities.
3. Experimental
Normal hydrogen (ortho-hydrogen, 75 %) was used as a Raman medium in this study, since it exhibits a marked Raman activity compared to other gases. The Raman shift frequencies for molecular rotation and vibration are 587 and 4155 cm-1, respectively. The periods of the rotation and vibration are inversely proportional to these values and are 57 fs and 8 fs, respectively. A laser beam emitted from a Ti:sapphire laser with a chirped pulse amplifier (CPA; 784 nm, 100 fs, 1 kHz, 1.6 mJ/pulse, Concerto, Thales Laser) was used as a fundamental laser beam. Thus, the pulse width of the laser beam is much longer than these periods. The diameter of the beam from the amplifier was reduced to 5 mm using a telescope consisting of a pair of plano-convex and plano-concave lenses. All lenses and windows used were composed of fused-silica. By passing the fundamental beam through a KDP crystal (KH2PO4, 44.5 degree, 1.5-mm thick, type I), a second harmonic beam can be generated. The fundamental (784 nm) and harmonic (392 nm) beams were used, respectively, as pump and probe beams. The beams are focused with a lens (f = 600 mm) into a Raman cell (800-mm long, 5-mm-thick windows at both ends) filled with hydrogen gas (10 atm). The laser beam was rather weakly focused in order to avoid breakdown in the hydrogen gas. The intensity of the pump pulse in the Raman cell is estimated to be 20 TW/cm2 even at the maximum. The output beams from the cell were collimated by another lens (f = 600 mm) and then passed through a color-glass filter or a pair of dichroic mirrors to reject the pump beam. The residual output probe beam was introduced into an optical fiber equipped with a multi-channel spectrometer (USB2000, Ocean Optics) to measure the spectrum or into a homemade self-diffraction frequency-resolved optical gating (SD-FROG) system [19,20] to analyze the temporal profile of the output probe pulse. In the SD-FROG system, a cover glass (120-170-μm thick, borosilicate, Micro Cover Glass, Matsunami Glass) was used as an SD medium, with a multi-channel spectrometer (USB2000) as the detector. The optical layout of the system is basically the same as to that described in Ref 20.
4. Results and discussion
4.1 Efficient generation of rotational Raman lines
Fig. 1. Experimental setup with optical delay lines; KDP, SHG crystal; TL, telescope; CF, color glass filter; λ/2, half-wave plate
It is important to investigate the factors affecting the efficiency of generation of a Raman emission to obtain a broad spectrum required for pulse compression. In this experiment, the optical layout shown in Fig. 1 was employed to change the pump and probe energies independently. After the second harmonic generation using the KDP crystal, the fundamental pump and the second-harmonic probe beams were separated with a dichroic mirror. In order to change the pulse energies, neutral-density filters (not shown in the figure) were inserted into both the beam passes. The pump beam was then passed through a half-wave plate (λ/2) and the polarization was rotated from the horizontal to the vertical by changing the angle. This half-wave plate was used to determine the time delay of zero, which was confirmed by observing the cross phase modulation signal between the vertically polarized pump and the probe pulses. After the optical delay lines, the two beams were aligned so as to be collinear using another dichroic mirror. The time delay of the input probe pulse from the input pump pulse was adjusted to 1.4 ps by translating the delay stage.
Fig. 2. Spectra of the output probe pulse measured at different pulse energies for the input probe (a) and pump (b) pulses. The energies of the probe (a) and pump (b) pulses are specified in the figures. Arrows indicate the generated rotational Raman lines.
Figure 2(a) shows the spectra for the output probe pulse obtained using a 540-μJ pump and 2.3~6.2-μJ probe pulses. Three rotational Raman lines arising from ortho-hydrogen are observed, and there is no appreciable change in these spectra. This suggests that the energy of the input probe pulse does not affect the efficiency of generation of the Raman emission, which is in good agreement with that expected from theory (see Sec. 2). The intensity of the Stokes emission is, however, not equal to that of the anti-Stokes emission, in contrast to that expected in Sec. 2. The observation of such an unsymmetrical shape in the spectrum would be expected, when two input beams (pump and probe) are not propagating collinearly but are slightly off-axis with respect to one another. In this case, the efficiency of generation of the anti-Stokes emission is not equal to that of the Stokes emission because of phase mismatching [21].
Figure 2(b) shows spectra obtained by changing the energy of the pump pulse from 330 to 540 μJ while that of the probe pulse remained constant at 6.2 μJ. In contrast to the case shown in Fig. 2(a), the spectrum, and thus the efficiency of generation of the Raman emission, change appreciably with the pump pulse energy; no emission line is observed at 330 μJ, while three emission lines are generated at 540 μJ. As described in Sec. 2, the efficiency of generation of the Raman emission for the probe beam is affected by the amplitude of the coherent molecular motion induced by the pump pulse. At the pump energy of 540 μJ, the efficiencies of the energy transfer from the fundamental peak to the 1st Stokes, anti-Stokes, and the 2nd anti-Stokes peaks are 6, 15, and 2%, respectively.
The setup used in the above experiment enables the time delay between the two (pump and probe) input pulses to be controlled. However, the pump pulse energy is substantially decreased by partial beam reflections at the two dichroic mirrors. In order to increase the pump pulse energy, the setup was modified slightly as shown in Fig. 3. The two dichroic mirrors causing the major loss of energy were removed from the apparatus. After passing the beam through the KDP crystal, both the fundamental pump and second-harmonic probe beams were directly focused on the Raman cell by a lens (f = 500 mm), and the output beams were collimated again by a lens (f = 450 mm). The probe beam was isolated using a dichroic mirror and was introduced into the SD-FROG system for measurement of the temporal profile.
The modification of the system led to an increase in pump pulse energy. In addition, the system is simple and easier to operate in this configuration, since the careful alignment of the beams is not necessary. Unfortunately, the time delay between the two pulses cannot be controlled and was fixed at an estimated value of 1.5 ps which was nearly identical to the 1.4 ps used in the previous experiment. The difference in the time delay (100 fs) has no significant effect on terms of generating the Raman emission, since the time delay is smaller than the dephasing time of the coherent motion of the hydrogen molecule and the pulse width of the probe beam used here (>100 fs) is sufficiently longer than the period of the coherent molecular motion.
Another important factor affecting pulse compression is the duration of the input pump and probe pulses. The efficiency of generation of Raman emission was then examined at different pulse widths (197~393 fs, FWHM) for the input fundamental laser by changing the degree of the negative frequency chirp by means of a grating-pair compressor located inside the Ti:sapphire CPA system. The duration of the input pump pulse was measured using a commercial autocorrelator (Pulse Check, Angewandte Physik & Electronik). Since the pulse width was changed before passing the beam through the KDP crystal, the energy of the second harmonic beam was also changed, as a result of the change in the efficiency for frequency doubling. In fact, the energy of the input probe pulse was changed from 5 to 16 μJ by changing the pulse duration from 393 to 197 fs, while that of the pump pulse remained at 960 μJ. The effect arising from the change in the energy of the input probe pulse can, however, be neglected in this study, since it does not have an appreciable effect on the efficiency of generation of the Raman emission, as described in the discussion of the data shown in Fig. 2(a).
The spectra of the output probe pulse obtained at different input pulse widths, shown in Fig. 4, contain a number of rotational Raman lines arising from ortho-hydrogen. When the negative frequency chirp of the input pulse is small (197 fs, FWHM), only three Raman lines are generated. In contrast, the number of the emission lines increase substantially with increasing pulse width. The efficiency approaches a maximum at 327 fs, at which ten rotational lines are observed. The efficiencies of the energy transfer from the input probe beam to the Raman sidebands of the 1st Stokes, anti-Stokes, the 2nd Stokes, and anti-Stokes emissions are 24, 23, 5, and 5%, respectively. A further increase in the pulse width (e.g., at 393 fs) decreases the efficiency.
Fig. 4. Spectra of the rotational Raman emission obtained at different pulse energies for the fundamental input beam and energies for the probe input beam specified in the figures.
The observed data, i.e., the dependence on the pulse width, can be explained as follows. A frequency-chirped pump pulse having a low peak power provides a lower efficiency in transient SRS than that achieved using a Fourier transform-limited pulse with a high peak power [18]. However, the efficiency of transient SRS is drastically decreased, when the peak power of the transform-limited pump pulse exceeds a certain level due to other nonlinear optical effects such as self-focusing or self-phase modulation. Therefore, a slightly chirped pulse, rather than a transform-limited pulse, was desirable for producing an efficient transient SRS in this study. This observation is in reasonable agreement with previously reported data [8].
4.2 Temporal behavior of probe pulse
The temporal profile of the probe pulse was measured by means of SD-FROG using the second experimental setup (Fig. 3). The energies of the pump and probe pulses were 850 and 39 μJ, respectively. As described in the previous section, a negatively-chirped input pulse was employed. The energy of the output probe pulse was 14 μJ, and the energy loss (25 μJ) of the probe pulse was mainly caused by reflections at the surfaces of the uncoated windows and lenses.
The FROG trace obtained in this study is shown in Fig. 5(a). The retrieved spectrum and phase are depicted by solid and dotted lines, respectively, in Fig. 5(b). The time-integrated spectrum, measured by using the multi-channel spectrometer, is shown as a dashed line in the same figure, in which three rotational Stokes and anti-Stokes lines arising from ortho-hydrogen can clearly be observed. The retrieved spectral phase consists of a parabolic curve, indicating a linear negative frequency chirp for the output probe pulse. The temporal profile retrieved from the FROG trace is shown in Fig. 5(d), suggesting the generation of a train of pulses consisting of a 23-fs-long (FWHM) main pulse and seven satellite pulses. The spacing between the pulses is 57 fs, identical to the period of molecular rotation for ortho-hydrogen. As shown in Fig. 5(b), the retrieved spectrum (solid line, hatched) is slightly different from the time-integrated spectrum (dashed line) in the vicinity of the first-order anti-Stokes line (384 nm). This may arise from a two-photon absorption by the borosilicate glass used as an SD medium, since two-photon absorption becomes stronger at shorter wavelengths. The change in sideband intensity affects the widths of the pulses in the train. The temporal profile calculated by the inverse Fourier transformation of the observed time-integrated spectrum is shown in Fig. 5(c), in which the probe pulse is assumed to be transform-limited. It consists of a train of 11-fs pulses, while the inverse transformation of the retrieved spectrum [solid line in Fig. 5(b)] provides a similar pulse train but the widths of the pulses are increased to 15 fs. These values (11 and 15 fs) are smaller than that obtained by the FROG analysis (23 fs) because of the negative-chirp of the pulse as is observed in the FROG trace [Fig. 5(a)] and in the spectral phase [dotted line in Fig. 5(b)]. The group delay dispersion (GDD), stretching the laser pulse from 15 to 23 fs, is estimated to be -95 fs2. The value of the group delay (GD) obtained from the position of the main peak observed in the retrieved temporal profile [Fig. 5(d)] is -30 fs. The retrieved phase [Fig. 5(b)] can not be reproduced precisely from the spectral phase calculated from these values (GDD = -95 fs2 and GD = -30 fs) at high-order Raman components. This is probably due to the weak intensities of the high-order Raman components, which provides insufficient contributions in the calculation of the retrieved phases. This error, however, does not provide a serious or undesirable effect in the calculation of the temporal profile. Given the GDD of -95 fs2, the inverse Fourier transformation of the time-integrated spectrum results in a pulse width of 26 fs, which is nearly identical to 23 fs obtained for the retrieved temporal profile [Fig. 5(d)].
The number of the sub-pulses obtained in the retrieved temporal profile [Fig. 5(d)] is different from that obtained by the inverse Fourier transformation of the observed spectrum [Fig. 5(c)]. The number of pulses in the train is not affected by the difference in the retrieved and time-integrated spectra but is changed by distortion in the spectral phase. This distortion increases not only the width of the individual pulses in the train but the width of the envelope of the pulse train as well, thus increasing the number of sub-pulses. Basically, the width of the pulses in the train is related to phase distortion among the Raman sidebands, while the number of the sub-pulses is related to phase distortion in each sideband; this subject has already been analyzed and has been discussed elsewhere based on inverse Fourier transformation [22]. It should be noted that two types of phase structures are observed in the FROG trace [depicted by arrows in Fig. 5(a)]; one arrow specified by a dashed line denotes phase distortion among the sidebands while the other arrow specified by a dotted line denotes the phase distortion in each sideband. Both of the lines indicate negative frequency chirps for the output probe pulse, although the degree of chirp (slope of the line) is different from each other.
Fig. 5. FROG analysis of the probe pulse. (a) FROG trace measured using SD-FROG. (b) measured (dashed blue line) and retrieved (solid red line, hatched) spectra; the retrieved spectral phase is shown as a dotted green line. (c) temporal profile obtained by inverse Fourier transformation of the spectrum shown in (b); (d) temporal profile retrieved from the SD-FROG trace. In (a), two types of frequency chirps are observed; an arrow with a dashed line denotes the phase distortion among the sidebands, while an arrow with a dotted line denotes the phase distortion in each sideband.
As described above, the increase in the number of the sub-pulses in the temporal profile is caused by the negative frequency chirp in each sideband, and the increase in the widths of the sub-pulses by the negative frequency chirp among the sidebands. The latter frequency chirp can be compensated by the insertion of a glass plate, which causes positive group delay dispersion. The former frequency chirp, however, can not be precisely compensated for using this glass plate. As observed in the FROG trace, the degree of frequency chirp in each Raman sideband is nearly identical to that of the fundamental component. The negative chirp may then be compensated by the insertion of a pair of prisms, which change the degree of frequency chirp of the input probe pulse. The combination of these two types of phase controls can be used to produce a train of pulses with shorter widths and a smaller number of sub-pulses than that obtained in this experiment.
A single ultrashort pulse can be obtained by using a shorter probe pulse (<57 fs) or by the contribution of para-hydrogen for the complete spectral coverage, which should be followed by proper compensation for the phase distortion; e.g., using a spatial phase modulator.
4.3 Generation of vibrational Raman lines
Vibrational Raman emission was generated, in addition to rotational Raman emission, by changing the angle of the KDP crystal slightly. In this experiment, the duration of the input pulse was changed from 175 to 262 fs, the energies of the pump and probe pulses being 880 and 62 μJ, respectively. The spectrum of the output probe pulse at different input pulse widths are shown in Fig. 6. Similar to the case for the rotational emission, the efficiency of generation of the vibrational emission changes significantly with a slight change in the pulse width of the input pump beam; the maximum efficiency was obtained at 193 fs, at which three vibrational Raman lines (S1, S2, and AS1) accompanying several rotational lines are generated. The efficiencies of the energy transfer from the input probe beam to the 1st vibrational Stokes, anti-Stokes, and the 2nd vibrational Stokes lines are 29, 1, and 1%, respectively. Since the frequency shift of the vibrational emission is larger (4155 cm-1) than that of the rotational emission (587 cm-1), a wide spectral domain can be covered, which is desirable for further compression to a few-cycle pulse. The inverse-Fourier transformation of the spectral data shown in Fig. 6(b) suggests that a train of sub-5 fs pulses can be generated. Further pulse shortening, e.g., to 1 fs, can be achieved by the generation of a larger number of vibrational lines. This may be an advantage of this method over other techniques based on broadband frequency doubling or self-phase modulation due to a wider spectral coverage from the far-ultraviolet to the near-infrared.
Fig. 6. The variation of the vibrational emission efficiency with the input pulse widths; the pulse width of input pump pulse is shown in figures. Arrows indicate the vibrational emission lines; F, S1, S2, and AS1 shows the fundamental (392 nm), first vibrational Stokes, second vibrational Stokes, and first vibrational anti-Stokes emissions, respectively.
5. Summary
A novel approach to pulse compression is described, based on a combination of transient SRS and a pump-probe technique. In contrast to the approach based on impulsive SRS, the present method does not require a short input pump pulse and has the potential for use in the generation of a sub-10-fs pulse with a simple, commercially available Ti:sapphire laser. In fact, a second-harmonic 100-fs pulse from a Ti:sapphire laser was compressed to sub-30 fs using a simple device without any compensation for phase distortion. Further compression to a 10-fs pulse will be possible by appropriately compensating for phase distortion in the output probe pulse. In theory, a train of sub-5 fs pulses can be generated using vibrational/rotational Raman emissions.
Acknowledgments
Y. K. thanks Dr. Frank Noack for helpful suggestions in construction and operation of the FROG system and for his kind supervision during the stay in Max Born Institute. This work was supported by Grants-in-Aids for Scientific Research and for the 21st Century COE Program, "Functional Innovation of Molecular Informatics" from the Ministry of Education, Culture, Science, Sports and Technology of Japan.
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