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We describe a femtosecond pulse shaper using a deformable membrane mirror. The pulses are measured with a real time second-harmonic-generation frequency-resolved optical gating system. Pulse shapes are modified according to a prescribed spectral phase. Accurate spectral phase design as well as pulse intensity modulation was achieved by using negative feedback mirror-surface control. Convergence to the chosen spectral phase design was typically achieved within several seconds.
©2003 Optical Society of America
1. Introduction
Femtosecond pulse shaping has been studied for a number of years, but only recently have diagnostic tools and phase-modulating components become available which enable truly programmable pulse control. Shaping is commonly achieved by placing a phase or intensity modulator such as a liquid-crystal display (LCD) array [1, 2] at the Fourier plane of a grating-based pulse compressor adjusted for zero dispersion, but this approach is limited by two main problems. Firstly, the LCD modulators in common use are pixelated devices and so introduce step-wise changes in spectral phase, leading to temporal sidebands and reduced pulse contrast. Furthermore, wavelengths impinging on the dead-space between pixels remain unmodulated, causing a pulse pedestal. The second issue concerns how to rapidly monitor the pulses from the shaper so as to calculate the appropriate drive signal for the phase modulator. Previously reported implementations using stochastic genetic or simulated-annealing algorithms and frequency-resolved optical gating (FROG) required between a few minutes [3,4] and 1.5 hours [5], reducing the versatility of the techniques as practical laboratory tools. A more attractive real-time method for achieving spectral phase modulation has been proposed based on polarization spectral interferometry (PSI) [6]. The PSI method makes it possible to track in real-time the exact spectral phase added to a pulse by a birefringent modulator, however the technique does not directly permit programmable pulse shaping unless a previously fully-characterized reference pulse exists and relies on pixelated modulation. In addition to the limitations already mentioned, many of the prior approaches reported for programmable pulse shaping [2, 4–6] have concerned amplified ultrafast lasers and in some cases the modulator used (for example the acousto-optic programmable dispersive filter of [5]) cannot be applied to shaping high-repetition-rate modelocked pulse sequences.
In the work described here we demonstrate real-time programmable pulse generation using spectral phase-modulation by a micro-machined deformable membrane mirror to shape 842nm pulses from a self-modelocked femtosecond Ti:sapphire laser. The exact pulse profile, amplitude and phase were measured using second-harmonic frequency-resolved optical gating (SHG-FROG) and viewed in real time with a typical refresh rate of 1 Hz.
Spectral phase design as well as temporal intensity-profile shaping was achieved using automatic negative feedback mirror control. Convergence of the actual pulse to the prescribed shape was typically achieved within several seconds.
2. Experimental configuration
2.1 Optical design of the pulse shaper
The pulse shaper (Fig. 1) was based on a dispersionless design incorporating a 1200 lines/mm diffraction-grating (30° blaze angle at 850nm) and arranged in a 2f configuration with a deformable mirror situated at the Fourier plane of a 500 mm focal length concave mirror. The deformable mirror was fabricated by OKO Technologies [7] and had a rectangular 11×39 mm aperture containing a 19-channel linear micro-machined deformable gold-coated membrane. With a minimum settling time of 2 ms and maximum deflection at the mirror center of ~6 µm the deformable mirror could produce a maximum spectral phase change of approximately ±40 radians. Pulses from a self-mode-locked femtosecond Ti:sapphire laser with a bandwidth of 11 nm and centered at 842 nm were coupled into the shaper and dispersed to form a line spectrum extending across most of the 39mm aperture of the mirror. The corresponding calibration was 1.31 nm/mm for spectral phase correction purposes. Programming a chosen curvature onto the mirror surface produced a change in the spectral phase across the pulse spectrum. The mirror surface distortion was controlled through nineteen 8-bit channels by sending one control byte per channel with a maximum value (255) corresponding to 285 volts.
Fig. 1. Schematic of the adaptive-optic femtosecond pulse shaper. DG: diffraction grating; CM: concave mirror; DM: deformable mirror; PC: personal computer
2.2 Video-Rate Second-Harmonic Frequency Resolved Optical Gating
The amplitude and phase measurements of the pulses leaving the shaper were made with a real-time second-harmonic frequency resolved optical gating (SHG-FROG) system at a repetition rate of 1 Hz (Fig. 2) [8].
The system comprised a dispersion-balanced scanning interferometer that included silver-coated hollow retro-reflectors and a thin beamsplitter (R1, R2 and BS). One of the retro-reflectors was static and the other was scanned at around 40 Hz using a piezo-electric translator (PZ). The retro-reflectors were adjusted so that the pulses emerged from the interferometer as two parallel but non-collinear beams and these were incident centrally on a concave gold mirror (M2). The focal path after the gold mirror was folded using a near-normal incidence reflection from a plane gold mirror which steered the beams past the curved mirror and into a Type I phasematched 200µm-thick beta-barium borate (BBO) crystal where they combined with a small crossing angle. A short focal length lens (L1) situated one focal length away from the crystal collimated the second-harmonic light and this was steered at Brewster-incidence into a SF59 prism (P) that dispersed the light spectrally. Prior to the prism an iris diaphragm was used to select the central SHG beam that was produced by mixing the pulses from opposite arms of the interferometer. After the prism a second lens (L2) located one focal length away was used to form a line-spectrum of the SHG light on the surface of a charged-coupled device (CCD) camera. The galvanometer mirror (GM) was scanned at the same frequency as the delay line but with an adjustable phase delay which compensated for the different impedances of the piezoelectric translator and galvanometer mirror and their associated amplifiers.
Our system used an image acquisition board to digitize the 640×480 CCD trace directly into a C++ program which was used for calibration and trace retrieval. Following acquisition, the software was constructed to automatically enter a retrieval mode which used the principal components generalized projections algorithm [9, 10]. For a 64×64 element re-sampling and retrieval grid size convergence was typically obtained in less than 50 iterations which corresponded to a time of under 250ms (Pentium 4 running at a clock frequency of 1.6GHz) and was therefore essentially instantaneous. By default, retrieval was configured to begin by using a randomized trial pulse but faster retrieval was possible by using a previously retrieved pulse as the initial guess. This feature was implemented by calculating the normalized RMS error difference, known as the “G number” [11], between the re-sampled and retrieved FROG traces. The initial guess pulse for a given retrieval was updated to match the previous best retrieved pulse, corresponding to that with the minimum G number. Another advantage of this procedure was that by seeding the retrieval with an earlier retrieved pulse the system maintained some memory of the sign of the spectral phase which helped to avoid flips in the pulse time direction, an inherent problem in the SHG-FROG technique. Scanning, acquisition, display imaging, trace quality detection, re-sampling and retrieval involved in the whole measurement process allowed a typical refresh rate of the pulse intensity and spectral phase on the computer screen of 1 Hz.
3. Pulse shaping using negative feedback
The system we developed exploits the fact that by using real-time exact pulse measurement we can cause the measured pulse spectral phase to influence the actuator voltages through a feedback loop that can be configured to drive the mirror towards a target spectral phase profile. The implemented method involved a free running negative feedback system based on iterative automatic mirror voltage correction where, for each iteration, the voltage correction was calculated according to the difference between the actual and the target spectral phase profiles.
Prior to the shaping process, we set the mirror to its mid-range and flat position (~λ/10) using voltages previously established by using a spatial interferometry measurement. Next we compensated the pre-chirped pulses coming from the laser by changing the position of the concave mirror (CM in Fig. 1) in the shaper in order to produce bandwidth limited pulses.
Our procedure for spectral phase design is illustrated by the schematic in Fig. 3 and, as a starting point, we applied a voltage perturbation with respect to the equilibrium condition at the middle of its dynamic voltage range in order to generate a random surface. Next, the pulse spectral phase was sampled using the SHG-FROG system and, based on the difference, Δφ(ω), between the actual and target spectral phase profiles, the program modified the existing set of actuator voltages by an amount related to the spectral phase difference through a weighting parameter K according to:
The process was repeated iteratively and, depending on the desired shape and weighting parameter value, the system was able to produce the target spectral phase typically in less than 30 seconds. During the process the system ran freely and continuously updated and stored the set of voltages giving the closest match to the target phase profile. We permitted the algorithm to tolerate N iterations without a reduction in Δφ(ω) before automatically returning to the best previous settings and continuing the process. This feature was necessary to overcome the inherent ambiguities present in SHG-FROG regarding the pulse time direction and the absolute sign of the spectral phase because in some cases the sign of the spectral phase inferred from the SHG-FROG measurement was incorrect and caused the system to drive the mirror in the direction of increasing Δφ(ω).
We found that the convergence speed and accuracy were improved by using a dynamic weighting parameter. Starting with a fixed value, the weighting parameter K was reduced as the RMS spectral phase difference, δrms(ω) (defined in Fig. 3), approached zero. As a result we were able to generate spectral phase designs with good accuracy for both near-transform-limited and highly-chirped pulses.
The layout of the pulse-shaper interface is presented in Fig. 4 and illustrates the different components involved in the shaper operation including SHG-FROG control and calibration, pulse visualization and the voltage and spectral phase design windows. The spectral phase was designed using 19 sliders that were spectrally separated by around 2.7nm according to the wavelength-position calibration given earlier and whose locations in wavelength corresponded to the positions of the mirror actuators. The RMS spectral phase difference between the programmed phase and that retrieved from the SHG-FROG trace, δrms(ω), was calculated by interpolating the phase design onto a 64 element one-dimensional array that was then compared directly with the array of the same size produced by the SHG-FROG algorithm.
When the prescribed spectral phase was large we were able to produce significant intensity modulation and create pulses with multiple peaks, sharpened leading or trailing edges and linear and higher order chirp. Some results are presented in Figs. 5–8 and in each figure the target spectral phase is shown in blue and the measured spectral phase in red. The actual δrms(ω) value is displayed in the yellow label below the spectral phase window with the global minimum corresponding to the best match displayed in the pink label.
Figure 5 demonstrates the application of the shaper to pulse compression with 250 fs (1/e) input pulses being compressed by a factor of 1.28 to have final durations of 195 fs. We also tested the ability of the shaper to create linearly chirped pulses and Fig. 6 illustrates the result of programming a near-quadratic spectral phase profile. In this case pulses with initial durations of 185 fs were linearly chirped to have durations of 262 fs. Two other cases of more complex spectral phase designs were also studied. Figure 7 shows the result of programming a near-sinusoidal spectral phase with a range of 1.6 radians, corresponding to a double-pulse with a pulse-separation of 288 fs. It was also possible to program considerable asymmetry into the pulse profile by using a near-cubic spectral phase design and Fig. 8 illustrates the pulses produced in this way.
Fig. 5. (1.14 MB) Movie of pulse compression: Before shaping the pulse incident on the pulse shaper was substantially chirped but after shaping to a flat target spectral phase the pulse was compressed.
Fig. 6. (579 KB) Movie of near-quadratic spectral phase design: Shaping started from an arbitrary pulse with a small amount of spectral phase distortion and converged on a near-quadratic target phase.
Fig. 7. (321 KB) Movie of nonlinearly chirped pulse design: The target spectral phase had a near-sinusoidal form corresponding to a double pulse.
Fig. 8. (1.035 MB) Movie of near-cubic spectral phase design: the target phase had an approximately cubic form that led to an asymmetrical temporal profile with one extended edge.
The high finesse of the design technique also made it possible to create pulse profiles very close to the bandwidth limit and accurate small-scale structuring of the spectral phase was demonstrated over a range of better than 0.1 radians. The effect of such changes in the spectral phase are not strongly manifested in the main pulse shape but can be seen in the pulse wings and in the spectral phase retrieved from the SHG-FROG trace. Results illustrating precise changes to the spectral phase are presented in Figs. 9–11 which illustrate high-precision compression (Fig. 9), the introduction of a small amount of linear chirp (Fig. 10) and nonlinear-spectral phase shaping with a range of only 0.1 radians (Fig. 11). The ability to precisely manipulate the spectral phase is important for applications which utilize the shaper primarily to re-profile the wings of a pulse.
Fig. 9. (942 KB) Movie of pulse compression at small resolution: Shaping began with a shorter pulse than used in Fig. 5 and the scales are adjusted to show higher spectral phase resolution. After shaping the spectral phase of the compressed pulse matched the target phase with a RMS difference of 4×10-5.
Fig. 10. (697 KB) Movie of near-quadratic phase design at fine resolution: Shaping started with an arbitrary pulse and converged to a near-quadratic target phase profile with a variation of ~0.1 radians across the pulse bandwidth.
Fig. 11. (819 KB) Movie of non-linear chirp design at a resolution of less than 0.1 rad: Shaping was started from a short arbitrary pulse and converged to a near-sinusoidal target profile. The shaped pulse was broadened by a small amount and showed extended wings.
Better resolution for movie display is available in the follow Internet address: http://www.phy.hw.ac.uk/resrev/ufast.
4. Conclusions
In summary, we have demonstrated a system allowing dynamic real-time spectral phase design and control based around a deformable membrane mirror which was incorporated in a dispersionless diffraction-grating-based pulse shaper. Rapid shaping was made possible by using real-time SHG-FROG pulse measurement. Different prescribed spectral phases were generated using an automatic feedback method. Depending on the particular target spectral phase design we were able to create pulses that were optimally compressed to the bandwidth-limit, multiple peaked, asymmetric or exhibited linear or higher order chirp. We were able to produce and control both small-scale (~0.1 radians) and large-scale (~1–2 radians) spectral phase designs with good accuracy. Typically the system was able to produce the desired spectral phase in less than 30 seconds.
Due to its versatility, low loss, speed and accuracy, the pulse designer system presented in this work should represent a useful tool satisfying the different requirements existing within the diverse user communities for whom femtosecond pulse shaping is of interest.
Acknowledgements
The authors gratefully acknowledge sponsorship of this work by the UK Engineering and Physical Sciences Research Council. The authors also acknowledge the technical support of Miguel A. García Arthur.
References and Links
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