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A broadband spectral comb is generated around the third harmonics of incident light with the nondegenerate, impulsively stimulated Raman scattering technique using ultrashort light pulses. The comb has a spectral width of more than 4000 cm-1, and its envelope becomes smooth as the light powers are increased. It consists of discrete lines, the spacing of which is equal to the frequency of the Raman-active phonon mode, even though the frequency of the phonon mode is far smaller than the frequency difference between the two incident light pulses. The multiline structure is generated with multiwave mixing by exchange of the impulsively stimulated phonon among the signals.
©2004 Optical Society of America
1. Introduction
The generation of ultrabroadband coherent light is one of the best practical successes of higher-order nonlinear optics. Ultrabroadband coherent light is expected not only to generate ultrashort light pulses but also to synthesize the light pulses with desired temporal profiles [1]. There are several methods to generate the ultrabroadband coherent light pulses [2–5]. Self-phase modulation is the most popular technique. Recently, a microstructure optical fiber was successfully used to generate a supercontinuum covering visible and near-infrared regions [2]. Strong ultrashort light pulse injection in gases is known to generate extreme higher-order harmonics [3–5]. It has been demonstrated that two-color excitation efficiently generates extreme higher-order harmonics by use of stimulated Raman scattering (SRS) when the frequency difference between the two incident light pulses is tuned to the frequencies of molecular vibrational or rotational motions [5]. These are the signals that result from the tandem coupling process among the two incident light and the coherent anti-Stokes Raman scattering (CARS) signals. These phenomena attract great interest for the purpose of generating subfemtosecond light pulses [6–8] and tailoring the temporal shape of the light pulses to control ultrafast transient dynamics [9–11]. A unique application of the coherent light pulse with broad spectral width has been proposed to serve as a highly stable oscillator for an all-optical atomic clock [12]. We have shown that the SRS process can be observed in solids and, at the same time, that it couples with the third-harmonic generation (THG) and a spectral comb with a smooth envelope is generated by mixing of the THG and the CARS signals [13]. These effects are significantly enhanced when the frequency difference of the incident light pulses is tuned to the phonon frequency. The generated signal consists of discrete lines, whose frequency spacing is equal to the CARS-resonant phonon mode. Under much higher power, effects from other higher-order nonlinearities come to the stage. In this paper, we demonstrate that a nonresonant, low-frequency phonon mode emerges to the center stage in lieu of the CARS-resonant phonon.
2. Experiment
The YFeO3 sample is made by use of the floating zone method. The sample is cut perpendicular to the growing direction. The sample thickness is ~150 µm, and a polished (11̄0) surface is used for optical experiment. The nondegenerate impulsively stimulated Raman scattering is carried out with the signal (ω1) and idler (ω2) beams from a femtosecond optical parametric amplifier (OPA) laser system, whose pump beam is an 800-nm light pulse from a regenerative amplifier. The pulse widths and the spectral widths of both beams are approximately 150 fs and 200 cm-1, respectively. The repetition rate is 1 kHz. The pulse energies are a few microjoules per pulse. The spot sizes on the sample are several tens of micrometers. Their peak powers are estimated to be from the order of 100 GW/cm2 to a few TW/cm2. The wavelengths are monitored by second harmonic spectra generated from a β-barium borate (BBO) crystal. The two noncollinear beams are focused onto the sample by use of a lens with a focal length of 20 cm and an angle of several degrees. Their polarizations are parallel to each other. To observe the accumulated spectrum, i.e., the angular integrated spectrum, the emitted signals are focused into a spot by use of two lenses. The signals are picked up by an optical fiber with a 200-µm core radius after being diffused by a frosted glass plate placed in front of the fiber. For the angle-resolved spectroscopy, the lenses and the frosted glass plate are removed and the optical fiber is set on an electrically controlled rotational stage, whose rotation axis is located at the sample. The distance between the sample and the fiber is 40 mm. The fiber is connected to a multichannel spectrometer.
3. Results
Figure 1 shows the spectra around THG when the relative delay between the two incident light pulses is changed. Their frequencies are set to be ω1=6593 cm-1 and ω2=5993 cm-1, and the frequency difference of the two light pulses Δω is 600 cm-1, which is enough to excite the 630 cm-1 A1g phonon [13,14] because of the finite spectral widths of the incident light. The origin of the delay is set at the moment when the ω2 pulse arrives earlier enough than the ω1 pulse. The light powers are 1.4 mW for the ω1 beam (P1) and 1.2 mW for the ω2 beam (P2). When the two pulses do not overlap, there are two distinct THG peaks. The 3ω1 peak is broadened to as much as 700 cm-1, whereas the 3ω2 peak is broadened only to 400 cm -1, owing to higher-order nonlinearity. As they overlap each other temporally and spatially, several new peaks appear. The spectrum depends sensitively on the relative delay, and an obvious asymmetry against ω1 and ω2 light is observed. When the ω2 pulse proceeds to the ω1 pulse, narrow peaks other than the third-order sum frequency peaks are observed. These narrow peaks are clear and stable temporally when the delay is from 100 to 170 fs as shown in Fig. 1. The spacing between the peaks is 275 cm-1, which is a little bit larger than but well agrees with the frequency 260 cm-1 of A1g phonon mode [13,14]. The sequence of narrow peaks with almost the same spacing is found also when the frequency difference is changed to 900 cm-1. At the delay 180 fs, the fine structure with 275 cm-1 spacing disappears and only the CARS resonant multiline structure is observed. When the delay is increased more and the ω1 pulse proceeds to the ω2 pulse, each peak broadens, the whole spectrum becomes dulled, and the emission becomes stronger than that when the ω2 pulse proceeds to the ω1 pulse. When the irradiation powers are low, the 275 cm-1 fine structure is not observed but the abrupt change from the well-separated multipeak spectrum to the dulled one remains.
Fig. 1. Spectra accumulated around THG against the relative delay of the light pulses. The origin of the delay is set at the moment when the ω2 pulse arrives earlier enough than the ω1 pulse. The thick lines (at 135 and 360 fs) give the spectra at the moment when the power dependence and the angle-resolved spectra are monitored. The frequencies of the excitation beams are set to be ω1=6593 cm-1, ω2=5993 cm-1, and Δω=600 cm-1. Excitation powers are set to be P1=1.4 mW, P2=1.2 mW.
The spectra for several excitation powers monitored at the delay of 135 fs, which is shown as a thick line in Fig. 1, are shown in Fig. 2. Here P2 is fixed to be 1.2 mW, and in Fig. 2(a) P1 is changed from 0 to 1.4 mW, whereas in Fig. 2(b) P1 is fixed to be 1.4 mW and P2 is changed from 0 to 1.8 mW. The top spectrum in Fig. 2(a), the one second-from-the-top in Fig. 2(b), and the one at 135 fs in Fig. 1 are measured under the same condition. When P2 is fixed to be 1.2 mW and P1 is increased, there appears first the third-order sum-frequency signal (ω1+2ω2) at 18,600 cm-1 as shown in Fig. 2(a). For P1 above 0.5 mW, peaks with narrow spacing become easily visible. The critical behavior is shown more clearly in Fig. 2(b). When P1 is fixed and P2 is increased, the peaks become sharper and the spacing becomes narrower above P2=1 mW. The spacing of the top spectrum is uniform and is 275 cm-1. A salient feature is that the intensities of the peaks balance one another and the envelope becomes smooth when the power is high, as is clearly shown in Fig. 2(b). The THG and the sidebands are no longer distinguishable from one another.
Fig. 2. Spectra for several excitation powers monitored at the delay of 135 fs, the moment at which is shown in Fig. 1 as a thick curve. (a) P2 is fixed to 1.2 mW and P1 is changed from 0 to 1.4 mW, (b) P1 is fixed to 1.4 mW and P2 is changed from 0 to 1.8 mW. The top spectrum in Fig. 2(a) is the same as the one second-from-the-top in Fig. 2(b). Each spectrum is shifted upward by the value of the excitation power scaled on the vertical axis.
The angle-resolved spectra at three typical delays are shown in Fig. 3. When the two incident light pulses are apart temporally from each other with sufficient duration, well-separated THG peaks are observed as shown in Fig. 3(a), which is monitored at the delay of -40 fs. The origin of the angle is set in the direction of the 3ω1 signal peak. The 3ω2 signal is observed at 2.8°. The spatial divergence of the THG beams are ~0.8°. Figures 3(b) and 3(c) are the ones at 360 and 135 fs, whose delay is shown by the thick curves in Fig. 1. When the relative delay is 360 fs, where the ω1 pulse proceeds to the ω2 pulse, the peaks are clearly separated in the frequency region as shown in Fig. 3(b), even though the accumulated spectrum has a dulled structure. Here, light signals are observed in the directions consistent with the wave vectors of the incident light beams, but their frequencies shift slightly. The spectral change is much more impressive when the ω2 pulse proceeds to the ω1 pulse. As is shown in Fig. 3(c), each peak splits to narrow peaks with the spacing of 275 cm-1. Their widths are ~150 cm-1, which is smaller than those of the incident light pulses. It is noted that each peak in Fig. 3(c) is not separated spatially, contrary to the multistep CARS, where the higher-order signals are emitted in different directions, which are defined by the phase-matching condition [13]. It is obvious that the peaks are grouped in several spots, which are emitted in the same directions of THG, the third-order sum frequencies, and the higher-order THG-CARS. Nevertheless, the wavelengths of each peak included in each spot are mostly the same among the different THG-CARS signals.
4. Discussion
There are three competing processes: THG, THG-CARS, and SRS. The dominant order of the nonlinearity becomes higher for the latter processes. Under weak irradiation, the lowest-order process, THG, is dominant. As the power increases, the higher-order processes take center roles. The multistep CARS process is a tandem four-wave mixing process among the two incident light and the step-by-step CARS signals [13]. The (n-1)th CARS signal with frequency ωn-1 is mixed with the two incident light pulses, and the nth CARS signal with ωn=ωn-1+(ω1-ω2) is generated as shown in Fig. 4(a). The THG-CARS is the mixing process of the multistep CARS and THG. The signals are generated by the annihilation of two incident photons from the final excited states of the multistep CARS process as shown in Fig. 4(b).
Fig. 3. Angle-resolved spectra at three typical delays (a) -40fs, (b) 360fs, and (c) 135fs in Fig.1. P1=1.4 mW and P2=1.2 mW. The origin of the angle is set in the direction of the 3ω1 signal peak.
Fig. 4. Schemes of (a) multistep CARS: the emitted signal ωn-1 becomes the seed of the next wave-mixing process, (b) multistep THG-CARS: multistep THG-CARS signals are generated by the annihilation of two incident photons from the final excited state of the multi-step CARS process.
The probability amplitude of the transition from the ground state to the first vibrational excited state is expressed as
with ξa=Ea-ω 1, ξg’=Eg+ωp-ω 1+ω 2-iΓp, and A′ denotes the electron-radiation interaction. Here Ea′s are the energies of the intermediate electronic excited states, Eg is that of the ground state, and g′ denotes the first vibrational excited state, while ħω p and Γp are the phonon energy and its relaxation rate, respectively. When the frequency difference of the incident light pulses is resonant with the phonon frequency ΩC and the incident light is strong enough, the transition probability from the ground state to the vibrationally excited state becomes close to 1. The CARS signal is then enhanced resonantly by exchange of the phonon. The intensities of the higher-order CARS signals achieve balance by exchange of the phonon mutually among these higher-order modes. When such a condition is satisfied, the spacing of the signals is the same as the phonon frequency and/or the frequency difference of the incident light pulses [13]. Under much stronger irradiation, the sidebands appear and the wavelengths of the peaks are locked to those with another uniform spacing as is shown in Figs. 1 and 3(c). The spacing is 275 cm-1, which is slightly larger than but agrees well with 260 cm-1 of the A1g phonon. Therefore, we can understand the power dependence of spectra and other experimental results as a competitive process between the CARS process resonant with the A1g 630 cm-1 phonon and the SRS process resonant with the A1g 275 cm-1 phonon.
It is well known that coherent vibrations are induced by the impulsive excitation using ultrashort light pulses, whose pulse duration is shorter than the period of the vibrations [15]. Two mechanisms are proposed for the generation of the coherent phonons, impulsively stimulated Raman scattering (ISRS) [15] and displacive excitation of coherent phonons (DECP) [16]. Because the duration of the light pulses are longer than the period of the stimulated phonon, each light pulse cannot excite solely the phonon. Here, if there are two distinct light pulses, the accessible spectral width becomes the convolution of those of the two pulses. Then the coherent phonon can be stimulated by the ISRS mechanism via cross excitation of the two incident light pulses. It is a race of survival, which the 630 cm-1 CARS-resonant phonon or the 275 cm-1 SRS phonon wins. In the case of conventional SRS usually excited by ns laser pulses, there is a principle of “the winner gets all.” No more than two Raman modes can coexist. This race depends not only on the frequency difference of the incident light pulses but also on the cross section and the relaxation times of the phonons, and so on. In the case of the impulsive excitation, because the durations of the light pulses are sufficiently short, the off-resonant 275 cm-1 phonon has a chance to take a portion of the energy before the CARS-resonant phonon gets it all. Because the SRS is the higher-order nonlinear process, the 275 cm-1 phonon gets more energy as the light pulse powers increase. At last, it takes over the role of the CARS-resonant phonon in Eq. (1) under sufficiently short and strong excitation. When the SRS signals mix with the incident light, the anti-Stokes signals are generated by the CARS process involving the 275 cm-1 phonon. Once the SRS becomes sufficiently strong, the mixing among various modes becomes efficient by exchange of this SRS phonon. This process is enhanced also by resonance. Finally the peak intensities balance mutually in the same manner discussed for the multistep THG-CARS process. It is notable that the spectral width of each peak is narrower than those of the incident light beams. It is known that the spectral width of SRS gain in forward direction is dominated only by the Raman spectral width and does not depend on that of the pump source [17]. This supports the conjecture that the multiline structure is promoted by the SRS phonon. The abrupt change of the overall spectrum at the relative delay of around the best overlap is observed even under weak excitation. The origin has not been well understood. This is an interesting problem but remains as a future problem in this paper.
In summary, a broadband spectral comb, whose spacing is less than the frequency difference of the incident light pulses, is generated in the visible region by the nondegenerate, ISRS technique with ultrashort light pulses. This spectral comb is generated from the multiwave mixing process by exchange not of the CARS-resonant phonon but of an impulsively stimulated phonon.
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