We report on an optical field synthesizer consisting of a CEO-phase stabilized octave-spanning Ti:sapphire laser oscillator, a double-LCD prism-based pulse shaper, and a SPIDER pulse characterization apparatus. This field synthesizer allows for generating pulses with durations as short as 3.6 fs and enables to control the electric field on a sub-cycle scale. Within the limits of the ultrabroad spectrum arbitrary spectral and temporal pulse shapes and pulse sequences can be realized. Together with the ability to stabilize the pulses with respect to their CEO-phase, this system forms a versatile tool for coherent control experiments of field sensitive processes and precision spectroscopy.
©2008 Optical Society of America
Over the last few years rapid developments in the field of ultrashort pulse generation have led to pulses with durations as short as a few optical cycles with octave-spanning spectra generated directly from laser oscillators at high repetition rates . Meanwhile carrier envelope offset (CEO) phase stabilization of such ultrashort laser pulses is done routinely [2, 3, 4, 5] and opens up for CEO-phase dependent experiments [6, 7, 8, 9], the generation of highly stable frequency combs  and high precision spectroscopy [11, 12].
Besides spectroscopic applications, ultrashort pulses and the corresponding broadband spectra are key to coherent control experiments due to their unique spectral and temporal features. By using pulse shaping techniques it is now possible to shape pulses for high-resolution CARS [13, 14, 15], femtosecond quantum control  and generate pulse envelopes with durations of less than two optical cycles and flexible pulse sequences .
The combination of CEO-phase stabilized pulses with few-cycle phase and amplitude shaping extends this approach to an optical field synthesizer allowing for total control of the electric field of the laser pulses on a sub-cycle scale. This opens up new potential nonlinear and high-field experiments such as the investigation of surface photoemission  or atomic population dynamics .
Here, we report on a unique combination of a CEO-phase stabilized Ti:sapphire oscillator that forms together with a prism-based double-LCD pulse shaper and SPIDER measurement apparatus a flexible few-cycle electric field synthesizer, which allows for octave-spanning manipulation of the spectral phase and amplitude of the CEO-phase stabilized input pulses. This computer controlled versatile system is capable of generating single-cycle field oscillations with durations as short as 3.6 fs, which are to our knowledge the shortest pulses ever generated from a laser oscillator, next to shaping arbitrary pulse shapes and sequences in the time and frequency domain for coherent control and CEO-phase sensitive experiments.
An application example shows the flexibility and performance of such a system and demonstrates that it is possible to achieve a high signal-to-noise ratio with low pulse energies even in the case of nonlinear spectroscopic pump-dump type experiments.
2. Field synthesizer
As mentioned before, an optical field synthesizer is a tool that allows for control of the electric field of femtosecond laser pulses on a sub-cycle scale. The electric field of such pulses is determined by the spectral amplitude and phase in the Fourier domain, together with the CEO-phase, which is the phase difference of the carrier oscillation and the pulse envelope, in the time domain. By manipulation of these pulse parameters, the pulse envelope and therefore electric field waveform underneath the envelope can be controlled.
Our few-cycle field synthesizer consists of a CEO-phase stabilized octave-spanning Ti:sapphire seed oscillator , a double-LCD spatial light modulator allowing for independent spectral phase and amplitude manipulation and a home-built SPIDER measurement apparatus for pulse characterization .
The data analysis is computer-based and allows for a direct feedback to the light modulator for applying the desired phase masks to the shaper.
2.1. CEO-phase stabilized octave-spanning seed oscillator
The laser system used as seed oscillator is a prism-less Ti:sapphire laser designed for soft aperture Kerr-lens mode-locking. A more detailed description concerning this oscillator can be found in , its schematic setup is illustrated in Fig. 1(a). The laser crystal is pumped by 532nm cw-radiation from a frequency doubled Nd:YVO4 laser (Coherent Verdi series). For intracavity dispersion management, broadband double-chirped mirror pairs (DCMPs) [18, 19] are used together with BaF2 substrates and a specially designed broadband output-coupling mirror.
The optical output spectrum of the laser is shown in Fig. 1(b). It covers more than one optical octave (spanning from 600nm up to 1200 nm), supporting a Fourier-limited pulse duration of 3.7 fs. Together with an average output power of about 100mW this feature makes the laser the ideal light source for few-cycle pulse shaping experiments, delivering an enormous spectral bandwidth with considerable power. At a pulse repetition rate of 80MHz the pulse energy is approx. 1.25 nJ.
To obtain full control over the electric field of the femtosecond pulses the oscillator has to be CEO-phase stabilized. Due to the octave-spanning output spectrum this stabilization can be done without any additional spectral broadening, using a f-to-2f self-referencing technique [21, 22]. In our case the spectral wings centered around 570nm and 1140nm are filtered from the output spectrum using a multi-chroic transmission filter. Except for the transmitted spectral wings most of the output spectrum is reflected unchanged and remains for subsequent experiments.
The transmitted IR-wing is doubled within a nonlinear crystal and brought to interference with the transmitted fundamental 570 nm-radiation. The detection is done with a highly sensitive avalanche photodiode. The obtained beat signal of the f-to-2f components is given in Fig. 2(a). The CEO-frequency (fCEO) is detected in addition to the laser’s pulse repetition rate (frep), located at 80 MHz. This CEO-beat signal exhibits a signal-to-noise ratio (SNR) of more than 30 dB in a 100 kHz resolution bandwidth (RBW) which is sufficient to phase stabilize the oscillator using a feedback loop (Menlosystems XPS) controlling the oscillators pump power via an acousto-optic modulator.
The phase-stabilized pulses were characterized with SPIDER to be as short as 4.4 fs at 90mW average output power, given in Fig. 2(b). The pulse compression was done with dispersion compensating mirrors.
2.2. Prism-based pulse shaper
Key element of our pulse shaper is a double-LCD spatial light modulator (SLM, Jenoptik SLM-S640d), capable of independently manipulating the spectral phase and amplitude of femtosecond laser pulses. This device features two separately controllable and mechanically precisely combined LCDs with 640 pixels  and is positioned in the center of a 4-f geometry  with parabolic focusing mirrors.
The overall pulse shaper setup is shown in Fig. 3. As mentioned before the setup is prism-based which allows maintaining the octave-spanning input spectra and features a quite high efficiency compared to other techniques such as grating-based pulse shaping .
For optimal performance the input pulse beam has to be adapted in terms of dispersion and geometry. For pre-compensation of the dispersive optics within the setup, especially the highly dispersive SF59 prisms, the input pulses travel through a fused-silica prism-sequence. The sequence is used in a double-pass at an apex distance of about 1.25 m. After that, the beam radius and its collimation are adapted using an all-reflective telescope.
Within the 4-f geometry a SF59-prism is used to spectrally disperse the input beam. This prism is located in the focal plane of a first focusing mirror, which essentially performs a Fourier-transform that converts the angular dispersion arising from the prism to a spatial separation at the focal plane , where the spatial light modulator is located. This allows for independently manipulating the now spatially separated optical frequency components of the incident femtosecond laser pulse. From this point on, the center part of the pulse shaper setup is symmetric using equal components and path geometries, guaranteeing the recombination of the frequency components into a single collimated output beam.
For proper operation the LCDs have to be calibrated with respect to a pixel-to-frequency mapping and applied voltage-to-phase dependence. In terms of amplitude shaping a linear polarizer has to be placed behind the 4-f arrangement to clean the undesired polarization from the shaped pulse beam. For phase-only shaping this polarizer can be disregarded.
After traveling through the overall shaper setup, the available spectral width is slightly reduced, given in Fig. 4(a). Compared to the input spectrum, see Fig. 1(b), the spectral edges are steeper. The optical throughput of the overall pulse shaper setup, as shown in Fig. 3, is approx. 50 %, mainly limited by the numerous mirror reflections.
As mentioned before, in our system pulse characterization is done with a home-built SPIDER apparatus. Both, data acquisition and pulse reconstruction are performed in real-time allowing for a direct feedback of the present pulse characteristics, which is essential for proper preparation and alignment of the system.
The shaper is controlled directly by the measurement software. Thus to shape e.g. a Fourier-limited pulse, the present spectral phase of the unshaped pulse is measured, inverted and applied to the displays. The shaping result can be investigated immediately. Such a shaped pulse with flat spectral phase is given in Fig. 4(b).
The pulse energy for seeding the pulse shaper is not limited to the low nanojoule regime, which is typical for broadband or octave-spanning Ti:sappire oscillators. With respect to the optics, damage thresholds and nonlinearities respectively, the shaper setup can be used with pulse energies up to some microjoule and in combination with any broadband light source in the present wavelength regime. From the experimental point of view e.g. high-energy CEO-phase stabilized broadband seed pulses from an OPCPA system [25, 26] would be applicable for a high-energy field synthesizer. This combination would open up for numerous experiments where higher pulse energies are indispensable.
3. Field synthesis results and discussion
First experiments using the above presented field synthesizer were performed by phase-only shaping. Nearly Fourier-limited pulses with a flat spectral phase are generated by applying the inverted measured spectral pulse phase to the shaper (see section above).
Also the CEO-phase stabilized pulses given in Fig. 2(b) could be compressed to their original duration using phase-only shaping.
In this configuration the system is a very efficient tool for flexible dispersion compensation and can balance e.g. the dispersion of up to 30mm bulk fused silica and thus the dispersion of input windows to vacuum chambers could be easily compensated together with other optics within the beam path. In comparison, a pulse compression setup realized with DCMs is usually only appropriate for one specific setup. Even for minimal changes a mirror sequence has to be adapted.
The power of a combined spectral phase- and amplitude-shaping with respect to the generation of ultrashort laser pulses is shown in Fig. 5. Here a pulse as short as 3.6 fs is generated by multiplying the input spectrum with a Gaussian filter function centered at 845nm what enhances the spectral wings compared to the center parts of the spectrum. The spectral phase is again shaped to be flat. This pulse, shown in Fig. 5(b), is to our knowledge the shortest pulse ever generated directly from a laser oscillator. Unfortunately, this amplitude mask has the drawback of losing considerably pulse energy because nearly 66% of the pulse power in the center of the spectrum is suppressed as illustrated in Fig. 5(a).
By using broadband CEO-phase stabilized amplified input pulses as mentioned earlier, this drawback of losing pulse energy is of minor importance. Hence pulses with durations well below 4 fs and energies of some microjoule could be generated in principle.
The electric field of the single-cycle pulse from Fig. 5(b) is shown in Fig. 6. Here the electric field oscillation for zero and π/2 CEO-phase is plotted below the square root of the pulse intensity envelope.
This pulse exhibits a maximum field contrast (maximum E-field amplitude difference between zero and π/2 CEO-phase) of about 4% and a contrast between positive and negative oscillation direction of 15 %. In contrast, a 4.4 fs-short pulse would exhibit only 3% for the maximum field contrast and 11% for the second case , whereas these values for a 7 fs-pulse are below 1% and 2%. This contrast enhancement for the ultrashort pulse durations paves the way for further experiments investigating carrier-envelope phase effects.
Besides the generation of ultrashort pulses nearly any desired spectral phase curve can be realized within the limits of the shaper, which are the pixel resolution, its dynamic range, and maximum phase shift. Figure 7 presents a pulse sequence of two 4.5 fs-pulses generated by a modulation of the spectral phase. The delay between the pulses can be easily tuned by changing the modulation frequency, whereas the input pulse duration is maintained. Such pulse sequences have already proven their potential in coherent control experiments .
Pulses with almost any desired spectral or temporal shape can be generated out of the ultrabroadband input spectrum. Figure 8 reveals a measurement with flat spectral phase and rectangular spectrum resulting in a sinc-shaped pulse in time. The measurement (solid line) matches nearly perfectly the calculation (crosses). This example shows the power of our system in terms of providing clean pulses with tunable spectrum from 600nm up to 1200nm out of one single broadband input spectrum.
4. Application example
The presented field synthesizer forms a flexible tool for numerous applications, even for low energetic input pulses. In this example the temporal structure of the input pulse is modified to influence and probe the evolution of a molecular sample, the laser dye HDITCP. This application demonstrates the capability and performance of the setup, which allows low-noise results for very low pulse energy in a nonlinear application. The pump-dump-type  experimentwas performed simply by software control of the shaper to investigate the evolution of the excited state wave packet in the laser dye.
For this experiment the input pulses do not necessarily have to be CEO-phase stabilized, what reduces the system to a waveform synthesizer.
The input pulse spectrum was divided into two parts and by introducing different group delays for the two spectral regions an adjustable time delay between both was generated. The spectral separation between the pulses is chosen that way, that the spectral components within the pump pulse (650nm–820 nm) match the absorption band of the dye, whereas the probe pulse (830nm–1150 nm) fits to the emission band.
The shaper’s output beam is focused into a probe-cell with HDITCP dissolved in ethanol (α=4cm-1) by a reflective objective. Stimulated emission is generated in forward direction, whereas fluorescence can be detected perpendicularly. To enhance the detection sensitivity, the probe pulse is modulated with an optical chopper inside the shaper covering only the spectral part of the probe. The fluorescence signal, shown in Fig. 9(a), is then detected using a lockin technique as a function of the software controlled time delay between the two pulses. For negative delay the probe pulse arrives earlier than the pump, the S1-level of HDITCP is not exited and no fluorescence change is observed. This behavior changes when the pump pulse arrives first and creates a non-equilibrium wave-packet in the excited state. Depending on the time delay the probe pulse can ”dump” some of the excited state population back to the ground state and the fluorescence signal is reduced.
From the structure of the time signal the contributing vibrational modes can be obtained by a Fourier-transform as depicted in Fig. 9(b). The position of the vibrational modes from  are plotted for comparison. It should be pointed out that the individual scans are highly reproducible and show very low noise. Even for low energy pulses (here approx. 0.2 nJ) a fluorescence change as low as 0.2% is easily observable.
In conclusion, we demonstrated for the first time an optical field synthesizer with sub-cycle resolution: A unique combination of a CEO-phase stabilized octave-spanning Ti:sapphire oscillator, double-LCD pulse shaper and SPIDER measurement system to control the electric field of few-cycle femtosecond pulses on a sub-cycle scale. Full control over the electric field is achieved due to the ability to manipulate the spectral phase and amplitude of those pulses together with their CEO-phase. This system is capable of generating the shortest pulses directly from a laser oscillator with pulse durations as short as 1.3 optical cycles. It forms a flexible tool to generate tailored few-cycle pulses and versatile pulse shapes and sequences with respect to the time and frequency domain for a variety of applications.
The author thanks VENTEON for supporting the development, and providing the components and optics for assembling the seed oscillator. The work was financially supported in Hannover by the Bundesministerium fr Bildung und Forschung (BMBF) under contract 13N8723 and the Sonderforschungsbereich (SFB) 407 by the Deutsche Forschungsgemeinschaft (DFG), and in Cambridge by the National Science Foundation (NSF) under contract ECS-0501478 and the Air Force Office of Scientific Research (AFOSR) under contract FA9550-07-1-0014.
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