Optimized control of generation of few cycle pulses by molecular modulation

Optics Communications 264 (2006) 454–462 www.elsevier.com/locate/optcom

Optimized control of generation of few cycle pulses by molecular modulation A.M. Burzo *, A.V. Chugreev, A.V. Sokolov Department of Physics and Institute for Quantum Studies, Texas A&M University, College Station, TX 77843-4242, United States Received 10 November 2005; accepted 17 March 2006

Abstract Production of subfemtosecond optical pulses or pulses with predetermined sub-cycle shape of electric field demands a broadband coherent light source of few octaves of bandwidth. Previous work has shown that such a broadband light source can be obtained by the molecular modulation technique. In this article, we review theoretical and experimental improvements in this area: from increasing the efficiency of the generation process by use of hollow waveguides to increasing the number of sidebands generated by the Raman additive technique, or by combined vibrational and rotational Raman generation. We find that stimulated rotational Raman scattering can be either enhanced or suppressed at proper detunings from vibrational Raman resonance in the same molecular ensemble. Ó 2006 Elsevier B.V. All rights reserved. Keywords: Ultrashort; Ultrafast; Stimulated Raman scattering; Molecular modulation; Raman generation in hollow waveguide

1. Introduction Generation of ultrashort optical pulses in the 5 fs regime can be achieved through means of nonlinear optical phenomena. Several key developments have led to this result: development of mode-locked solid state laser technology [1,2], self phase modulation effect [3,4] which allowed the spectral broadening of the mode-locked pulses, and dispersion control by pulse shapers and by chirped mirrors [5–7]. Time-resolved measurements with these pulses allow to trace dynamics of molecular structure but fail to capture electronic processes occurring in atoms on an attosecond timescale. Therefore, in order to gain access to processes of this nature, it is necessary to break the few-femtoseconds limit which is imposed by the solid state mode-locked techniques [8]. New methods for obtaining subfemtosecond pulses have been proposed. Their common theme was Fourier synthesis of a large, equidistant spectral comb of frequencies with bandwidth up to 1015 Hz and adjustable

*

Corresponding author. E-mail address: [email protected] (A.M. Burzo).

0030-4018/$ - see front matter Ó 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.optcom.2006.03.076

individual phases. Generation of attosecond pulses in the soft X-ray regime, based on high harmonic generation (HHG) has been reported experimentally [9–12]. In HHG, a laser pulse and intensity around 1014 W/cm2 (comparable to the atomic field) is focused into a jet of rare gas atoms. More than 200 of (odd) harmonics could be generated, from a driving field wavelength of 800 nm down to 20 nm [9]. An alternative approach based on high-order stimulated Raman scattering (SRS) has also been suggested. Imasaka and colleagues have demonstrated the generation of broad rotational and vibrational Raman spectra in molecular hydrogen and discussed the possibilities of phase-locking this spectrum [13,14]. A sequence of 3.8 fs compressed pulses produced by time-varying refractive index in an impulsively excited SF6 has also been reported [15]. In related work, Kaplan predicted the existence of 2p Raman solitons with a phase-locked spectrum that Fourier-transforms into a train of subfemtosecond pulses [16]. By taking advantage of the maximum coherence obtained in a molecular diatomic gas subjected to a pair of fields that drive a Raman transition slightly off resonance [17], a large bandwidth of frequency components has been generated [18–21]. This new technique, called

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molecular modulation, differs from the standard SRS where only one field is applied. In addition, a low pressure gas is used (lower than atmospheric pressure), as opposed to high pressure exceeding few atmospheres in traditional SRS. The resultant comb of equidistant Raman sidebands has been used to synthesize controlled trains of ultrashort sub-optical-cycle pulses [22,23]. A similar scheme was demonstrated experimentally and theoretically in solid hydrogen [24,25]. The ability of making measurements in attosecond time regime opens new areas of science: from probing the motion of inner shell electrons to controlling fast ionization processes [26]. However, accessing and controlling processes that occur on a time scale of 100 attosecond requires a strict control over all parameters defining the optical pulse. The important parameter that governs the time evolution of such ultrashort pulse is the carrierenvelope phase [27], commonly referred to as the absolute phase. The importance of the absolute phase was demonstrated in many different applications, such as frequency metrology [28] or above threshold ionization processes [29]. Not a long time ago the control achieved in this direction represented a huge step forward in the attosecond field [30]. Various aspects of this field have been reviewed, for example, in [31]. Our paper is organized as follows: Section 2 contains a brief review of the molecular modulation technique initially proposed theoretically in [18,19] and realized experimentally in [21], and further theoretical developments already proposed in [32]. Section 3 describes in detail new results of Raman generation in a hollow waveguide filled with deuterium. In Section 4 we reveal new and exciting results of simultaneous generation of rotational and vibrational sidebands with only two fields applied, results which will be shown in detail in future papers, and the last part of the paper contains our concluding remarks. For clarity purpose, our overview of the molecular modulation techniques will address only the nanosecond regime, which results in production of trains of ultrashort pulses. A discussion of a possibility to generate isolated single-cycle pulses can be found, for example, in [33]. 2. Theoretical overview The central feature of the molecular modulation technique is the preparation of an ensemble of molecules in a coherent state – a feature that has also been used in various other applications, including electromagnetically induced transparency [34,35], ultraslow light propagation [36,37], lasing without inversion [38–40] and proposals for analytical chemistry and the detection of pathogens [41]. This coherent superposition of a ground state and first excited vibrational (or rotational) state in diatomic molecules is achieved by a pair of nanosecond lasers with enough intensity such that the product of their Rabi frequencies exceeds the product of the detuning from the electronic states and the detuning from the Raman transition. These two fields drive an ensemble of molecules either in phase, or 180°

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out of phase with their beat note frequency, depending on the sign of the (small) Raman detuning, and make all molecules in a macroscopic sample oscillate in unison. When the atoms in each molecule are stretched apart, the index of refraction increases, while in the case when they are compressed the index of refraction decreases. This periodic change in the index of refraction results in the modulation of driving field frequencies, and hence generation of a broad spectrum of sidebands [42]. The total bandwidth generated through this method extends from infrared and visible into the UV region, i.e., spanning over more than 50,000 cm1. When combined, the frequency components of such wide bandwidth comb synthesize trains of pulses separated by the molecular modulation period. Each train consists of pulses with different absolute phase, since driving field frequencies are generally incommensurate. In a theoretical proposal called Raman additive technique [32] we have suggested that trains of identical pulses (same absolute phase) can be obtained by applying input fields with frequencies chosen in such a way as to correspond to an integer multiple of the modulation frequency. Applying more input fields as proposed, for example, in [43] results naturally in an increase of the spectral density, simply because each of the individual applied field will produce sidebands that will add up in their number (hence Raman additive technique name). When used for pulse shaping, a denser comb is preferred, since the accuracy of shaping the temporal waveform is determined by the number of frequency components. The increase in the number of sidebands produced by the Raman additive technique is given by a multiplicative factor M. Although this factor M could be in principle arbitrarily large, in practice it will be restricted to two values (4 or 9). This constraint comes from the fact that necessary input driving field frequencies are generated through nonlinear frequency mixing processes such as second harmonic, third harmonic, and sum frequency generation. For generating a comb of frequencies spaced by 1/4 of the modulation frequency, two fundamental fields with frem quencies xf ¼ f x4m ; xf þ2 ¼ ðf þ2Þx are applied. In addition 4 to these fields, their second harmonics x2f ¼ 2f 4xm ; x2f þ4 m m ¼ ð2f þ4Þx , and the sum frequency x2f þ2 ¼ ð2f þ2Þx are gen4 4 erated and sent into the same cell [32]. Here f should be restricted to f = 4n ± 1, where n is a positive integer. This condition is crucial for generating interleaving sidebands at intervals separated by exactly xm/M = xm/4. The Raman transition is driven by the second harmonics of the fundamental fields at a modulation frequency xm given by the difference of the second harmonic frequencies. The fields are shown in Fig. 1(b). For comparison, the schematics of the old technique is rendered in Fig. 1(a). Details of this technique are given elsewhere [32]. Results of numerical simulations for hydrogen using both the additive technique and the ‘‘old’’ approach are given for comparison in Fig. 2. We model the generation process

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Fig. 1. Energy level schematic (top) for establishing coherence qab in a molecular system. jai is the ground state and jbi is the excited molecular state. The Raman detuning Dx is set by the driving laser frequencies. The detuning from the electronic states jıi is large and comparable to the applied laser frequencies. Bottom figure show applied input fields in the ‘‘traditional’’ molecular modulation technique (a), and in the Raman additive technique (b) for the case when M = 4. Frequencies of fields in (a) are given by xq = x0 + qxm, where xm represents the frequency difference of applied fields E0 and E1, and q is an integer. Frequencies of fields in (b) are labeled by xq ¼ q x4m , where xm represents here the frequency difference of the applied second harmonics fields and q = 4n ± 1, with n a positive integer. Ef is the electric field envelope at the applied fundamental frequency xf ¼ f x4m , and f = 4n ± 1, with n a positive integer.

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numerically for a vibrational Raman transition in H2 (xm = 4160 cm1). The generated combs of frequencies are obtained by solving the propagation equations for laser fields together with density matrix equations for the Raman transition. As mentioned before, this transition is driven by all combinations of fields such that their frequency difference is equal to the modulation frequency [32]. The results of the simulation are shown for comparison, with only two input fields (Fig. 2(a)–(c)) and with five fields (Fig. 2(d)–(f)). After the phases of these sidebands are

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adjusted (by an external pulse shaper), they synthesize a train of single-cycle pulses, with a repetition rate equal to the molecular frequency (Fig. 2(c)). This result is similar to Fig. 7 from Ref. [42], which considered sideband generation in D2. Fig. 2(d)–(f) shows the results for the same cell length and pressure, and five input fields applied at 1068, 874, 480, 534, and 437 nm. A four times increase in the spectral density is shown in Fig. 2(e) compared to Fig. 2(b). After phase-locking, these sidebands synthesize a train of single-cycle pulses (Fig. 2(f)) with a four times increased repetition period, and an increased intensity (compared to Fig. 2(c)). The same idea can be used for generating even denser combs, separated by one ninth of the molecular modulation frequency xm [32]. Using pulse shaping techniques one can engineer subfemtosecond pulses into complex optical signals according to specifications [44,45]. Many techniques have been developed that allow generation of such complicated optical waveforms: from liquid-crystal spatial light modulators [46], deformable mirrors [47], or scanning over a fixed mask [48], to acousto-optical modulators [49]. The updating rates of the various pulse shaping devices is typically of order of milliseconds (or 10 ls at best). However, very recently [50] it was shown that by using an electrooptical gallium arsenide optical phased-array modulator with 2304 controlled waveguides it is possible to achieve shaping of femtosecond pulses with updating rates of the order of 30 ns, many orders of magnitude faster than with previous techniques. This fast-rate shaping capability combined with a large number of adjustable channels gives hope that femtosecond Fourier-domain pulse shaping could be used to control all frequency components of, for example, typical femtosecond mode-locked oscillators. The range of applications of such shaped pulses is quite large today, ranging from femtosecond microscopy

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Fig. 2. Comparison of spectra obtained by applying two input fields (parts (a–c)) and five input fields with proper frequencies (parts (d–f)). The applied spectrum is shown in parts (a) and (d), and the output spectrum is shown in parts (b) and (e) (assuming an H2 cell of 6.8 cm length, 1 atm pressure at room temperature). The Raman detuning is 0.7 GHz for parts (a–c) and 0.5 GHz for (d–f). The instantaneous power density versus time after phase correction is shown in parts (c) and (f). The inset of (f) gives jE(t)j2 on a finer time scale, showing an individual single-cycle pulse with a subfemtosecond duration [adapted from Ref. [32]].

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and spectroscopy [51,52], to coherent control of atomic processes [53], nonlinear optical processes in semiconductors [54], and chemical reactions [55]. The creation of ‘‘designed’’ laser pulses and their use in attempts to control molecular events is a current frontier research area, giving hopes for the ultimate goal of ‘‘bond-selective chemistry’’. An example of such pulses is given in Fig. 3, where the amplitudes of the generated comb of Fig. 2(e) have been manipulated to create optical pulses with predetermined shape of the electric field. 3. Coherent Raman generation in a hollow waveguide filled with deuterium As described in previous work [42], the molecular modulation technique allows, by adiabatically driving a Raman medium, to generate a wide, phase coherent, spectrum of equidistant sidebands. Control of adiabaticity is achieved by detuning of the frequencies of driving lasers by a small value. There are several requirements for efficient generation of such a broad spectrum. Among them, a high enough intensity of driving fields of order of the several GW/cm2 (for few-nanosecond pulses typically). A good quality of transverse beam profiles of driving fields is also important for efficient spatial overlap. In addition, the interaction length has to be increased, since the generation process is proportional to the product of density and length. It is well known that focusing of laser beams in free space is restricted by diffraction [56]. The intensity of a laser beam is approximately constant over a range equal to twice the Rayleigh range. For low energy of driving fields, focusing to a smaller size in order to maintain the necessary intensity will reduce interaction length, and in consequence will reduce the efficiency of the generation process. One solution for achieving high intensity at lower power of input fields, while maintaining a long interaction length

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and a good quality of the beam profile could be the use of a hollow waveguide. These waveguides consist of a hollow tube (usually a glass capillary), which can be coated on its inner surface with a reflective material such as Ag. They are a good alternative to solid core fibers because of the air filled core that allows a high laser threshold power, together with low insertion loss, no end reflection and small beam divergence. Initially developed for medical and industrial applications involving the delivery of CO2 laser radiation, hollow waveguides have been used to transmit incoherent light for broadband spectroscopic and radiometric applications [57]. They are especially useful for nonlinear generation in gases, since they may be filled with a gas of choice. However, there are limiting factors in using hollow waveguides as shown by [58]. These limiting factors come from transmission losses due to bending (proportional to 1/R, where R represents the bending radius) and attenuation losses proportional to 1/a3, where a is the bore radius. Therefore, waveguide losses will increase as the bore radius is decreased, an effect which limits the bore size of the waveguide that can be efficiently used. Despite of these deficiencies, they still remain a better alternative for Raman generation than focusing in free space. Previous work has shown that efficient impulsive [15] and two-color [59] Raman generation can be achieved in a hollow waveguide in the femtosecond regime. Efficient collinear Raman generation requires phasematching (2kq  kq+1  kq1 = 0, where kq is the propagation constant for the qth sideband). As shown before, this condition translates into a requirement for group velocity (GV) matching among the sidebands [60]. Optimization of conditions for an efficient Raman generation involves an optimization of gas pressure, since GV may be different for frequencies of driving fields and the generated comb. Thus, the idea is to minimize the combined dispersion of the gas (positive) and waveguide (negative) and reduce the group velocity dispersion of generated sidebands in the region of interest. Dispersion in a Raman gas media is given by nq ¼ 1 þ N haq =e0 ;

ð1Þ

where e0 represents permittivity of vacuum, N is the number of molecules per volume, and aq is a dispersion coefficient for the generated qth sideband (given in Ref. [42]). For the lowest-order waveguide mode HE11, dispersion depends on both propagating wavelength k and bore radius a [61]  2 1 1:2k2 nWG ¼ 1  : ð2Þ 2 cp2 a Ultimately, compensating the group velocities reduces to adjusting the medium concentration for a given bore radius. Once the waveguide diameter is chosen, optimum pressure (i.e., gas concentration) can be calculated. Fig. 4 shows three different group velocity curves in the region of our interest 650–1064 nm for three different pressures with a

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1.8 1.7 10,000 12,000 14,000 Frequency (cm-1) Fig. 4. For a fixed waveguide geometry, there is an optimum pressure that compensates for group velocity dispersion (GVD). Here the waveguide radius is 160 lm and the optimum pressure corresponds to 450 Torr in the region of interest 650–1064 nm. The curves correspond to the case when the waveguide is filled with molecular deuterium.

fixed waveguide geometry (bore radius of 160 lm). The gas of choice here is molecular deuterium, and dispersion coefficients aq were calculated as in [42] for a set of frequencies spaced by about 3000 cm1, assuming that each sideband is propagating alone, and all molecules are in the ground state. Then, after the k vectors are calculated for these fixed frequencies, we interpolate their values for intermediate frequencies, and take a derivative of the interpolating function to calculate group velocity. In the case of multiple co-propagating sidebands, the propagation constants will be affected by sideband cross-coupling, which could result in a change of the optimum pressure. In addition, when dephasing becomes significant, the choice of the optimum pressure becomes a compromise between the pressure necessary to compensate for GVD and the pressure limit imposed by the collisional dephasing. Naturally, a larger molecular coherence can be established by driving a Raman transition with narrow linewidth (bandwidth limited) laser pulses with duration shorter than the dephasing time. As it was previously shown in [20], the use of collinear rotational Raman generation has significant advantages over vibrational generation. Among them, a smaller repetition rate of pulse trains could allow for single pulse selection. We are therefore choosing to drive v00 = 0, J00 = 2 ! v 0 = 0, J 0 = 4 transition in molecular deuterium at room temperature with two transform-limited ns Ti:Sapphire laser pulses at wavelengths of 782.33 and 807.56 nm. At room temperature, the population of J = 2 state is 42%, compared to, for example, 66% of the population found in the J = 0 state at liquid nitrogen temperature.

For the S0(2) (v00 = 0, J00 = 2 ! v 0 = 0,J 0 = 4) transition, collisional half-width in molecular deuterium at room temperature is about 36 MHz at 450 Torr pressure, and is increasing proportionally to the density as shown in [62], to about 57 MHz at 704 Torr. The two Ti:Sapphire lasers are synchronized and combined on a beam splitter and sent into a 1 m long fused silica hollow fiber with 160 lm radius, filled with molecular deuterium at pressures between 300 and 750 Torr at room temperature. The light produced in the cell is dispersed by a pair of fused silica prisms and projected onto a white screen. Both lasers are home-build injection seeded from external-cavity diode lasers and pumped by the second harmonic of the same Quanta-Ray Q-switched Nd:YAG laser. Output energies and pulse durations (around 5 ns) are comparable to each other, and are comparable to the dephasing time at our working pressures. We estimate that the pulse duration corresponds to about 90 MHz transform-limited linewidth (which is still somewhat larger than the collisional half-width within our working pressure range). All beams are almost linearly polarized, with ellipticity of 0.04 for the 782 nm laser and 0.08 for the 807 nm laser. We use a polarizer to measure the angle of the polarization plane with respect to the p-plane for the Brewster windows of the D2 cell (this p-plane is horizontal in our experiment). We find that the polarization plane of the 782 nm beam is rotated by 10° with respect to this horizontal direction, while the polarization of the 807 nm beam makes an angle of 14° (clockwise direction, looking in the direction of propagation, is defined as negative). For comparison, the same experiment was repeated by focusing the two beams in free space using a Raman cell of the same length at the same pressure and same input energies. In both cases (free space and waveguide), these input energies were 5.5 mJ/pulse for the 782 nm laser and 8.6 mJ/pulse for the 807 nm laser. The transmitted energies through the waveguide were 2.8 and 1.6 mJ/pulse, respectively. Assuming that the coupling was into the lowest-order mode, the intensities of the two beams inside the waveguide were 1.72 GW/cm2 for the 782 laser, and 1.1 GW/cm2 for the 807 laser. In the free space case, the beam sizes were optimized (increased) for maximum generation, and the focused beam sizes were measured to be 230 and 265 lm, which gave intensities of 0.66 GW/cm2 for the 782 nm laser, and 0.77 GW/cm2 for the 807 nm laser. Dispersed output of the fiber is presented in Fig. 5 at a small positive detuning from the Raman resonance, where the generation process is optimized [63]. For comparison, we present rotational spectrum generated in the hollow fiber (Fig. 5(a)), and in free space (Fig. 5(b)). Driving fields are indicated by E1 and E0; we kept the same notation as in, for example, Ref. [42]. It is easy to see that the use of the hollow fiber improves the efficiency of the generation process. Fig. 6 shows the output spectrum as taken by an Ocean Optics SAS-series spectrometer. When these sidebands are phase-locked, pulse trains with a repetition rate of 12.4 THz can be achieved.

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Fig. 5. Rotational spectrum produced in molecular deuterium at 704 Torr pressure. (a) shows the spectrum generated in a hollow fiber, while (b) shows the Raman spectrum generated in free space. Driving fields are indicated in both (a) and (b) by E0 and E1.

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Fig. 6. Rotational Raman generation in a hollow-core fiber filled with molecular deuterium at 704 Torr pressure. Driving fields are indicated by E1 and E0 (dashed lines). Due to the limited range of the spectrometer, not all of the generated sidebands are displayed.

4. Intriguing recent results: rotational and vibrational Raman generation with two fields While the previous idea (the use of a hollow fiber) will allow a more efficient Raman generation, an increase in the spectral density of the generated comb is desired for a better control over the electric field. Our theoretically proposed Raman additive technique can be implemented by applying two independent tunable lasers, together with additional fields obtained by harmonic generation and frequency mixing. A related idea of obtaining a multiplicative increase in the number of sidebands has been investigated theoretically [63] and very recently experimentally [64]. That technique was based on the use of modulators in series that allowed generation of a large number of non-equidistant sidebands in a cell filled with different species. The experimental setup that we describe here is similar to the one described in [21]. However, unexpected new results were observed: namely simultaneous rotational and vibrational Raman generation in deuterium gas, with

only two laser pulses applied at the input of the molecular cell. Only the fundamental vibrational transition Q1(0) (v00 = 0, J00 = 0 ! v 0 = 1, J 0 = 0) is driven strongly in this experiment. However, in addition to efficient vibrational Raman generation we observe generation of a large number of rotational sidebands corresponding to the S0(0) (v00 = 0, J00 = 0 ! v 0 = 0, J 0 = 2) transition. We have investigated the effects of the temporal, spatial, and angular beam overlaps on generation efficiency and transverse beam quality. To our surprise, we observed that under certain conditions strong vibrational Raman generation leads to efficient rotational generation, while under different conditions the vibrational Raman generation may suppress a self-starting stimulated rotational Raman generation. The experimental setup consists of two lasers with a tunable frequency difference corresponding to the Q1(0) transition in deuterium, which are synchronized and sent into a cooled Raman cell at pressures between 50 and 750 Torr at 77 K (the corresponding Doppler-width is about 250 MHz [42]). The first laser is a transform-limited Q-switched injection seeded Nd:YAG laser (Quanta-Ray 6350) with pulse duration of 12 ns at a repetition rate of 10 Hz. The second laser is a 10 Hz repetition rate injection seeded tunable Ti:Sapphire laser with pulse duration of about 5 ns. Polarizations of the two driving fields are linear, with ellipticity of 0.08 corresponding to the 807 nm beam and 0.03 for the 1064 nm beam. We measure that the polarization plane of the 807 nm beam is rotated by 14° with respect to the horizontal p-plane for the Brewster windows of the Raman cell, while the polarization of the 1064 nm beam makes an angle of 2° (clockwise, looking in the direction of beam propagation). A typical spectrum of the generated light is presented in Fig. 7. The spectrum consists of lines corresponding to the pure fundamental vibrational transition at 2994.6 cm1 and rotational lines corresponding to the lowest rotational transition S0(0) with a separation frequency of 179 cm1. The origin of the rotational generation is stimulated Raman scattering (SRS) of the (more powerful) 1064 nm laser, which is replicated to all other vibrational sidebands through a ‘‘cascading’’

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process. We observe the onset of SRS by the Nd:YAG laser at pressures above 250 Torr, and energies above 180 mJ/ pulse. However, we observe that at a fixed pressure, given energies of driving fields, and a particular detuning, rotational generation completely disappears, while at a different detuning from the vibrational Raman resonance a four orders of magnitude enhancement of rotational generation is achieved. To illustrate these two particular cases, we present two spectra, together with their corresponding pictures. The first case, presented in Fig. 8 shows a pure vibrational comb, while Fig. 9 shows the rotational generation superimposed onto the vibrational comb. The only differ-

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Fig. 7. The generated spectrum in molecular deuterium as recorded by a spectrometer (Ocean Optics HR4000CG-UV-NIR). The spectrum was obtained by a combination of molecular modulation as described in Ref. [21] (with efficient excitation of the Q1(0) vibrational transition) and SRS of the S0(0) rotational transition. Detuning from the vibrational Raman resonance is of order of Dx = 1.6 GHz. The 807 nm laser energy is 8 mJ/ pulse, while energy of the 1064 nm laser is 240 mJ/pulse, and D2 pressure is 300 Torr. The inset shows the unsaturated spectrum obtained by reducing the intensity by a factor of 100.

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Fig. 8. The generated spectrum in molecular deuterium consisting only of vibrational lines at a near-zero detuning from the vibrational Raman resonance. The 807 nm laser energy is 8 mJ/pulse, while the energy of the 1064 nm laser is 180 mJ/pulse, and D2 pressure 300 Torr. (a) A picture of the dispersed spectrum taken with a digital camera, while (b) shows the same spectrum as recorded by a spectrometer (Ocean Optics HR4000CGUV-NIR).

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Fig. 9. The generated spectrum in molecular deuterium under the same conditions as in Fig. 8, but at a positive detuning from vibrational Raman resonance of around 1 GHz. (a) A picture of the dispersed spectrum taken with a digital camera, while (b) shows the same spectrum as recorded by the spectrometer. The inset shows the rotational comb spaced by 179 cm1.

ence between the two cases is the detuning from the vibrational Raman resonance (near-zero in the first case, and a positive detuning of around 1 GHz in the second case). The position of the vibrational Raman resonance was established by scanning the Ti:Sapphire laser frequency and measuring the first anti-Stokes sideband generation at the 650 nm wavelength at three different pressures in the Raman cell (84, 170 and 289 Torr). The linear shift of the Raman resonance with pressure was determined then by extrapolation and used to calculate the Raman resonance at 300 Torr pressure. The efficient generation close to the Raman resonance is not too surprising. Even though earlier work has shown suppressed collinear Raman generation when the Raman detuning is zero [21], it has been pointed out that such suppression appears when the laser linewidth is narrower than the inhomogeneous Raman line broadening. When shorter laser pulses are used (like in our present experiment) the resonant suppression may become less dramatic. This is similar to the situation when the pulses are kept longer but a smaller-frequency narrowerDoppler–width Raman transition is used, like in the recent experiment by Yavuz et al., where negligible resonant suppression was observed for rotational Raman generation in molecular hydrogen [63]. We note that at near-zero detunings we do see a slight drop in the anti-Stokes conversion efficiency, but still observe significant broadband generation, as shown in Fig. 8. A more detailed look at the origin of the behaviour of rotational generation will be given elsewhere [65]. Nonetheless, an important aspect is shown here – namely the interconnection of the two processes: collinear Raman generation and stimulated Raman scattering. The intriguing interplay of vibrational-rotational generation could be related to ultrashort pulse compression in the same molecular medium, which was predicted in our earlier work, or it

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can be a signature of EIT-like intra-molecular quantum interference, or maybe due to Raman self-focusing [66]. Simultaneous rotational and vibrational generation may improve ultrashort pulse compression, as shown in [64]. 5. Conclusion Generation of reproducible attosecond pulses is an exciting goal. In this paper, we have suggested ideas that will allow improving one scheme for obtaining such ultrashort pulses: the molecular modulation technique. In a theoretical proposal called Raman additive technique, we have suggested a method that will allow (with a proper phase stabilization of the generated sidebands) to obtain reproducible waveforms of arbitrary shape. An exciting range of possibilities could open up – not only for the absolute phase control or the sub-cycle shape control, but also for the investigation of multiphoton ionization rate as a function of the sub-cycle shape. Employing shorter pulse durations of the driving fields than previously used [42], while maintaining comparably high pulse energy, led to the establishment of large molecular coherences at higher operating pressures than in previous experiments. This resulted in simultaneous generation of multiple rotational and vibrational sidebands with only two fields applied. In another experiment using the rotational transition in deuterium we have shown that employing a hollow waveguide instead of a normal Raman cell improves the efficiency of the generation process. By optimizing the gas pressure and the waveguide geometry to compensate the dispersion, this method can be extended to efficiently generate Raman sidebands at a much lower energy of driving fields than previously employed. Acknowledgments The authors thank Dr. Gerhard Paulus for providing the V groove chamber used in the hollow waveguide experiment, M. Zhi, L. Naveira, J. Peng for their help with the experimental setup, and Yu. Rostovtsev and P. Anisimov for helpful discussions. This work has been supported by the National Science Foundation (Award No. PHY-0354897), an Award from Research Corporation, and the Robert A. Welch Foundation (Grant No. 1547). References [1] U. Keller, Nature 424 (2003) 831. [2] F. Krausz, M.E. Fermann, T. Brabec, P.F. Curley, M. Hofer, M.H. Ober, C. Spielmann, E. Winter, A.J. Schmidt, IEEE J. Quantum Elect. 28 (1992) 2097. [3] U. Morgner, F.X. Ka¨rtner, S.H. Cho, Y. Chen, H.A. Haus, J.G. Fujimoto, E.P. Ippen, Opt. Lett. 24 (1999) 411. [4] K. Yamane, S.D. Silvestri, O. Svelto, R. Morita, M. Yamashita, Opt. Lett. 28 (2003) 2258. [5] R. Szipo¨cs, K. Ferencz, C. Spielmann, F. Krausz, Opt. Lett. 19 (1994) 201.

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