1. Introduction

It is well known that the creation of shaped optical pulses requires phase coherence across the entire spectral bandwidth of the signal being shaped. In its simplest form, arbitrary pulse shaping consists of taking an already coherent spectrum, generated by a single mode-locked laser, and manipulating the phases and intensities of its constituent frequencies. Pulse-shaping using spatial light modulators [1] is a well-developed embodiment of this approach but is limited by the available bandwidth of a single laser. This restriction can be overcome by the use of multiple mode-locked lasers producing pulses with different centre wavelengths [2]. Such sources normally generate pulses that are neither synchronised in their repetition frequencies, nor phase-coherent, since their carrier-envelope phases evolve independently; however, electronic feedback methods are capable of synchronizing pulses from separate lasers having widely-separated spectra to within 100 as [3] and of locking the carrier-envelope phase-slip (CEPS) with an accuracy of 10 as [4]. Shelton et al [5] showed such a level of precision to be sufficient for the synthesis of optical pulses from coherent mode-locked spectra by combining pulses from two independent lasers having overlapping spectra centred at 760 nm and 820 nm with a coherence time of 20 ms.

In multiple-laser schemes, the greatest challenge is to obtain sufficient stabilisation of the repetition frequencies to allow coherent combination of the pulses over significant time periods. In contrast, schemes making use of a femtosecond synchronously-pumped optical parametric oscillator (OPO) ensure robust passive synchronization between all of the pulses, which together can span more than 3 octaves of bandwidth [6]. The problem for coherent synthesis is then reduced to locking the CEPS frequencies of all the participating pulses to a common value. Using this scheme we previously demonstrated coherent synthesis between two outputs from a femtosecond OPO centred at 1240 nm and 1330 nm [7], and stabilized the CEPS frequencies of the various outputs of a mode-locked laser and OPO, spanning 400–2400 nm [8]. In the present paper we report the creation of phase-coherent pump and frequency-doubled signal pulses, and we verify their mutual coherence through cross-correlation and spectral interferometry measurements made with both pulses tuned to a common centre wavelength of 780 nm. Although coherence can be asserted from radio-frequency measurements that indicate the same CEPS frequency for each pulse sequence, directly interfering the pulses in the time and optical frequency domains provides the strongest test of their coherence.

2. Experiment

The optical arrangement of our experiment is shown in Fig. 1. The self-mode-locked Ti:sapphire pump laser generated 55 fs pulses with a centre wavelength of 800 nm, a full-width-half-maximum bandwidth of 20 nm, and a repetition frequency a 200 MHz. The output beam had an average power of 1.25 W and was split by partial mirror M1, with 0.25 W being focused into a photonic crystal fibre (PCF) to generate a super-continuum spectrum covering 520–1060 nm. This spectrum was used as a reference to measure the CEPS frequency of the pump pulses by using an f-to-2f non-linear interferometer [9].

The remaining 1.0 W of pump power was down-converted in a femtosecond OPO by quasi-phase matching (QPM) in a crystal of periodically-poled lithium niobate doped with 5% magnesium oxide (MgO:PPLN). The OPO was operated close to degeneracy, with signal and idler pulses at 1560 nm and 1640 nm respectively, but was tunable across the wavelength ranges 1300–1570 nm and 1630–2080 nm. Weaker but highly visible green pulses at 529 nm and 538 nm were generated in a non-phase matched secondary process of sum-frequency mixing (SFM) between the pump and the signal or idler respectively. Some of this green light leaked backwards through input coupler M4 and was used to obtain the signal CEPS frequency in a second interferometer by isolating the 529 nm pump-signal SFM light with a 3 nm bandwidth interference filter (not shown) and optically heterodyning it with the pump super-continuum reference spectrum.

 

Fig. 1. Optical layout. BBO, beta barium borate crystal. CLx,y cylindrical lenses. FM, flipper mirror. IF, interference filter. P, polariser. PBS1-3, polarising beam splitters. PCF, photonic crystal fibre. PD, photo-diode. PZT1,2, piezo-electric transducer.

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The signal second-harmonic (SH) output was chosen for the experiment because of its overlap with the pump spectrum. To achieve sufficient power at this wavelength we configured the OPO for intra-cavity frequency-doubling of the signal using a 5 mm thick, antireflection-coated crystal of beta-barium-borate (BBO). Approximately 15 mW of the intra-cavity SHG beam left the cavity through focusing mirror M7. Being astigmatic, this beam was collimated using separate cylindrical lenses CLx and CLy. Using a 10 nm bandpass interference filter IF we extracted pump pulses centred at 780 nm, having 10 mW average power, from the unsed pump spectrum transmitted by mirror M5. Pump and signal SH pulses were overlapped at polarising beam-splitter PBS3 by adjusting the pump pulse delay with piezo-actuator translation stage PZT2, which also provided scanning for the cross-correlation measurement.

 

Fig. 2. Locking scheme for stabilising the CEPS frequencies of the pump and signal pulses. Red and green solid lines: optical. Black dashed lines: electronic.

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For interference to be observed between the pump and SH signal pulses, they must have the same repetition frequency F, to ensure overlap between successive pulse pairs, and the same CEPS frequency, to ensure a constant phase difference between the two carrier waves. The lack of gain storage in a synchronously-pumped OPO guarantees tight locking between the pump and signal pulse repetition frequencies. Therefore, to obtain coherence between the pump and SH signal pulses it is sufficient to lock only their CEPS frequencies to a common value. This assumes that the timing jitter between the pulses, due to differences in the lengths of their separate paths to the detector, is not significant (but see Results and Discussion).

The frequency-locking scheme employed is shown in Fig. 2. The pump and signal CEPS frequencies monitored in the two interferometers (Fig. 1) were compared with reference frequencies using separate digital phase-frequency detector (PFD) circuits [10]. The frequency references, F/4 and F/8 respectively, were derived using a frequency divider from the laser pulse repetition frequency F, which was monitored by a fast photodiode. Locking the signal CEPS frequency to F/8 ensured that the SH signal CEPS frequency was F/4, the same as the pump. The outputs from the PFD circuits were used to lock the pump and signal CEPS frequencies by means of, respectively, a travelling-wave acousto-optic modulator to modify the power in the beam pumping the Ti:sapphire laser [11], and a piezo-electric transducer (PZT1; 320 kHz unloaded resonant frequency) to apply fine (~10 nm) adjustments to the OPO cavity length [12]. The FWHM bandwidths of the CEPS frequency beats derived from the two interferometers were both ~3 kHz when locked to the reference frequencies, compared to 500 kHz (Ti:sapphire) and 8 MHz (OPO signal) when free-running.

3. Results and discussion

With the CEPS frequencies of the pump and SH signal pulses locked to the same value we observed deep fringes [Fig. 3(a)] in the combined optical spectrum measured on a fast scanning spectrometer (IST Rees; 30 Hz update rate), indicating strong coherence between the two sources during the sweep time of 4 ms. When the CEPS frequencies were unlocked the spectrum was smooth, indicating a lack of phase-coherence between the pulses. The individual spectra of the pump and SH signal pulses are shown in Fig. 3(b) for comparison. The maximum observable visibility was limited by imperfect matching in wavelength and intensity between the pump and SH signal spectra, the limited resolution of the spectrometer (0.3 nm), and the different beam sizes and divergences of the two sources.

The period of fringes in the spectral interferogram, which is sensitive to differences of path length between the two beams, changed from one sweep to the next, 30 ms later. This suggests that our assumption that the two sets of pulses arrive at the detector with the same repetition rate was not fully valid. The two beams followed separate paths between the PPLN crystal and beamsplitter PBS3 (see Fig. 1), over which there was no common-mode rejection of mirror vibrations, resulting in a timing jitter between them. This jitter could be reduced by active control of the path-length difference, but a passive solution, such as optimizing the optical path common to both pulses, is preferred.

Interferometric cross-correlation between phase-locked pulses provides a complementary time-domain measurement which is extremely sensitive to their mutual coherence [13]. The cross-correlation was obtained in real-time using fringe-resolved two-photon detection [14] in a 635 nm AlGaInP laser diode (PD in Fig. 1) and resulted in a trace with high-contrast fringes (Fig. 4). The scan rate was 5 Hz and the oscilloscope sweep time was 20 ms. Figure 4(a) shows the full trace plotted on a scale where the baseline is normalised to unity. The contrast ratio is around 6:1, but unlike an auto-correlation trace the deviation from an 8:1 ratio does not indicate the presence of incoherence, only that the powers of the input pulses were not exactly balanced. Figure 4(b) is a magnified portion of the trace showing the difference in the interference fringes under locked (orange) and unlocked (black) conditions.

The spectral interferometry and cross-correlation measurements show that mutual coherence was maintained for periods of at least 20 ms (maximum sweep time) up to around 100 ms (period between screen shots). We believe that the coherence times of the individual pulses were limited by cycle-slips in the locking loop of the OPO resulting from acoustic noise coupled through the optical bench and into the OPO cavity.

 

Fig. 3. (a). Single-shot spectral interference between SH signal and pump pulses with CEPS frequencies both locked to 50 MHz and unlocked. The sweep time was 4 ms. (b) Pump and SH signal spectra, recorded independently of the measurement in (a).

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Fig. 4. (a). Second-order cross-correlation between the pump and SH signal pulses, recorded with their CEPS frequencies locked to 50 MHz (orange lines) and unlocked (black lines). (b) Expanded detail of fringes around zero delay.

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Fig. 5. Phase noise power spectral density (PSD) of the pump (a) and OPO signal pulses (b) when the CEPS frequencies of both pulse sequences were locked to 50 MHz.

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The origins of phase noise within the locking loops can be inferred from the power spectral density (PSD) of phase fluctuations in the pump and signal CEPS frequencies. These measurements are shown in Fig. 5 and imply that acoustic noise around 200 Hz dominates in the laser output, as found by Fortier, et al [15], while in the OPO there is, in addition to the laser noise, significant broadband acoustic noise at 20–500 Hz, together with prominent resonances at harmonics of 30 kHz associated with the piezo-mounted mirror. The phase noise accumulated over the acquisition time of 1 s was 2.0 rad for the laser and 6.9 rad for the OPO, which implies that limitations in the quality of the locking were primarily responsible for limiting the individual coherence times of pulses. The PSD results indicate coherence times for the pump and signal pulses, relative to the reference signal, of around 0.1 ms, but their mutual coherence was maintained for much longer (20 ms or more) because noise present in the laser is copied in the OPO, so it is common to both beams.

A likely source of acousto-mechanical noise in our set-up, as seen in the PSD, was the fan in the Verdi laser driver unit. This was rigidly coupled to the optical bench via an umbilical cord, but siting the Verdi laser head on a separate bench would be problematic for us. Noise may also arise from variations in the output power of the Verdi laser. We assume that any such noise is compensated by the fast feedback of the AOM (Fig. 2). Phase noise caused by air currents was reduced by covering the pump laser, OPO and non-linear interferometer with Perspex boxes, but evacuation of these boxes might also be necessary.

4. Conclusion

We have generated two coherent pulse sequences by locking the CEPS frequencies of pulses from a femtosecond OPO and its pump laser to the same sub-harmonic of their common repetition rate. Spectral interferometry and cross-correlation measurements showed that coherence between them was maintained for periods of 20 ms or longer. In-loop phase-noise spectra of the locked CEPS frequencies indicated that acousto-mechanical noise dominated in the system output.

Such coherent pulses can be used to synthesize optical waveforms by direct interference of their electric fields. We expect modifications to the apparatus and locking electronics, mentioned above, to reduce phase noise and timing jitter and extend the mutual coherence between the pulses to several seconds. With the CEPS frequencies of the pump and signal pulses locked to zero, the laser-OPO system would then be suitable for coherent synthesis of identical pulses from its multiple, tunable, milliwatt-level outputs covering a wide spectral bandwidth.