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Carrier-envelope-offset (CEO) and pulse-repetition frequencies of a Ti:sapphire-pumped femtosecond optical parametric oscillator were locked to uncertainties of 0.09 Hz and 0.16 mHz respectively, with the CEO beat signal linewidth being stabilized to 15 Hz (instrument limited). In-loop phase-noise power spectral density measurements showed a contribution of our servo electronics to the comb-line frequency uncertainty of up to 110 Hz. Complementary time-series data implied an in-loop comb instability of 2 x 10−11 (1-s gate time), matching the Rb-stabilized reference used and verifying that dual servo-control of the CEO and repetition frequencies was effective in stabilizing the comb to at least this precision.
©2011 Optical Society of America
1. Introduction
Stabilizing the CEO-frequency (fCEO) in ultrafast optical parametric systems is an area of research currently attracting great interest. Techniques for achieving this include using optical parametric chirped-pulse amplifiers [1], and passively stabilized optical parametric amplifiers [2, 3]. Another method of obtaining fCEO-stabilized pulses is using synchronously-pumped optical parametric oscillators (OPOs). These are versatile sources of tunable near and mid-infrared (IR) pulses [4], and stabilizing their fCEO enables their application in coherent pulse synthesis [5] and broadband frequency comb generation [4, 6–10].
Previously we reported a simple Ti:sapphire-pumped OPO which produced a near-IR fCEO-stabilized output without f-2f self-referencing [11]. This system does not require a phase-stabilized pump laser, so an OPO frequency comb can be implemented with the Ti:sapphire fCEO free-running and with only its repetition rate (frep) and fCEO of the OPO signal pulses being stabilized. Here we present frequency-stability measurements from this system which allow its performance to be compared with that of competitive near-IR combs. Phase-noise and two-sample frequency deviation measurements, obtained with the system referenced to a precision Rb-disciplined quartz oscillator, allow us to estimate the in-loop comb instability, providing the first evaluation of the suitability of such an OPO comb for optical frequency metrology and high-resolution spectroscopy applications.
2. Experimental configuration
The comb was based on the system in [11], in which a 6-W Spectra-Physics Millennia VIsJ laser was used to pump a Ti:sapphire crystal in a four-mirror ring cavity which produced 50-fs pulses with 1.4 W average power centered at 793 nm and a repetition-rate of 280.18 MHz. A beam-splitter after the laser output coupler was used to couple 25% of the laser output into a photonic crystal fiber (PCF) for supercontinuum generation. The OPO was a 4-mirror ring cavity based on a 1-mm magnesium-doped periodically-poled lithium niobate (MgO:PPLN) crystal (HC Photonics. grating period 20.4 μm) and was synchronously pumped using the remainder of the output from the Ti:sapphire laser. When fCEO was locked it produced <130 fs pulses at 1500 nm (35 nm FWHM bandwidth) with an average power of up to 105 mW. Some of the pump + signal sum-frequency mixing (p + s SFM) light reflecting from the crystal surface and leaving the cavity along a different path to the main beam (see Fig. 1 ) was combined with the supercontinuum in the interferometer and detected at an APD to give fCEO for the signal pulses (fCEO(meas)).
Fig. 1 Schematic of the optical layout: M, dielectric mirrors; GTI, Gires-Tournois interferometer mirror; OC, output couplers; PZT, piezoelectric transducer; PRM, partially-reflecting mirror; PCF, photonic crystal fiber; PBS, polarizing beam-splitter; IF, interference filter; PL, polarizer; PD, photodiode; APD, avalanche photodiode; Amp, amplifier; LPF, low-pass filter; BPF, band-pass filter; SSG, synthesized signal generator.
We detected frep of the Ti:sapphire laser, (equal to frep of the OPO) using a fast Si photodiode (PD) placed in the depleted Ti:sapphire beam leaking from M4 of the OPO cavity (frep(meas)). The 8th harmonic of frep (~2.24 GHz) detected by the PD was isolated using a band-pass filter to provide one input to a frequency mixer. An Agilent E4411B synthesized signal generator (SSG1) with its output set to 2.24144 GHz (frep(ref)) was used as the other mixer input, the output of which was passed though a proportional-integral (PI) amplifier to provide a signal to the piezo-electric transducer (Fig. 1, PZT1) in the Ti:sapphire laser cavity. The repetition rate remained locked for up to 1 hour with no adjustment of frep(ref).
We locked fCEO of the signal pulses by using the method reported in [11]. The signal fCEO (fCEO(meas)), detected at the APD was amplified, filtered and passed though a comparator to provide an input to one channel of a phase-frequency detector (PFD) [12]. The 10-MHz reference from SSG1, fCEO(ref) entered another comparator to supply the second input of the PFD. The PFD output was amplified in a PI amplifier to actuate PZT2, which controlled fCEO. The stage on which M5 was fixed could be adjusted using PZT3 (the same model as PZT1) to manually tune the OPO wavelength and move fCEO to within the capture range of PZT2.
3. In-loop phase-noise power spectral density measurements
The contribution of our servo electronics to the comb-line frequency instability can be estimated from in-loop phase-noise power spectral density (PSD) measurements of frep and fCEO, with the lower-limit determined ultimately by the sensitivity of the phase-noise measurement system used. With frep locked, the fCEO beat frequency was observed on a radio-frequency (RF) spectrum analyzer, and its signal-to-noise ratio and −3-dB bandwidth provided immediate indicators of the quality of the fCEO locking. In Fig. 2 we present the RF spectrum of the stabilized fCEO recorded with a frequency span of 2 kHz, a sweep time of 20 s and a resolution bandwidth of 10 Hz. The measured fCEO beat had a −3 dB bandwidth of 15 Hz and a signal-to-noise ratio >35 dB. This result improves on our previously reported bandwidth by two orders-of-magnitude [11], and even now shows stability comparable to the 10 Hz resolution of our RF spectrum analyzer. This performance surpasses that of other comparable near-IR combs including a Cr:forsterite laser at 1.25 µm (ΔfCEO ~1 MHz) [13], and Er-doped fiber lasers at 1.53 µm (ΔfCEO ~600 kHz) [14], however Er-doped fiber combs using strongly-driven laser-diodes and phase-lead compensation control can achieve sub-Hz linewidths [15].
Fig. 2 RF spectrum of fCEO, recorded while frep was locked, with a span of 2 kHz (200 kHz inset). The −3 dB bandwidth is 15 Hz with an instrument resolution of 10 Hz.
Measurements of the in-loop phase-noise of fCEO allow an estimate of its contribution to the comb-line stability to be made, and can be used to diagnose the degree of cross-talk between the fCEO and frep locking loops. Part of the output of the PFD used for locking fCEO was recorded using a 12-bit data acquisition card. An amplifier before the card ensured we filled its dynamic range, however this amplifier also contributed noise to the measured results, limiting the minimum fCEO phase-noise which could be measured to 4 mrad (integrated over the full frequency range). The data were taken for 1-s periods, with and without frep stabilization. The output from the PFD was calibrated in phase to give the phase error between fCEO and the 10 MHz reference, so the noise in this signal can be analyzed to know at which frequencies the most significant noise contributions to fCEO lie. With frep locked, the cumulative phase noise of fCEO was 0.56 rad, whereas without frep locked this error reduced to 0.52 rad – a small change, showing that stabilizing frep did not significantly reduce the quality of fCEO locking. Similar in-loop phase-noise measurements of frep were also made, and in this case the measurement-system contribution to the frep phase-noise was 0.06 mrad. The phase-noise PSD for frep and fCEO are shown in Fig. 3 .
Fig. 3 In-loop measurement (1 s observation time) of the phase-noise PSD for (a) fCEO and (b) frep. The integrated phase-noise from 1 Hz - 2 MHz is 0.56 rad (0.98 mrad) for fCEO (frep). (b) The PSD phase-noise for frep is shown for the 8th harmonic, and the integrated data are scaled appropriately to show the cumulative phase-noise in frep.
The data in Fig. 3(a) indicate an increase in the fCEO phase-noise PSD between 10 kHz (corresponding to the corner frequency, fc, used on the PI amplifier) and 100 kHz, which we attribute to the mode competition and beating effects resulting from the use of a multi-longitudinal-mode pump laser. The relative intensity noise this causes couples into the Ti:sapphire laser – and therefore the OPO – increasing the phase-noise present [11, 16]. Figure 3(b) shows that a significant contribution to the phase-noise in frep occurs between 100 Hz (the fc used on the PI amplifier) and 1 kHz, which is likely to be close to the bandwidth limit of the locking loop. The cumulative frep phase-noise integrated from 1 Hz – 2 MHz was 0.98 mrad, which corresponds to an uncertainty in frep of 0.16 mHz. A similar calculation for fCEO gives an uncertainty of 0.09 Hz. For an optical frequency, fn, of 200 THz, the corresponding mode number, n, is 714285, implying a contribution of our feedback electronics to the uncertainty in the comb line position of 110 Hz and indicating that the uncertainty in fCEO has a negligible impact. This value can be considered an upper limit since it also contains contributions from noise in the phase-noise measurement system.
4. Two-sample frequency deviation and in-loop comb instability measurements
Time-series frequency-stability measurements were made to characterize the effectiveness of our servo-control system and its contribution to the comb instability. The implementation used a frequency counter to record the variation in frep and fCEO while locked over a range of gate times, from which we calculated the two-sample frequency deviation of these signals.
A Rb reference was used to stabilize a synthesized signal generator (SSG1) which in turn was used to stabilize SSG2 and a frequency counter, as shown in Fig. 4 . The Rb clock had a long term fractional stability of < 2 x 10−11 / day and a short term stability of 9 x 10−13 over 100 seconds [17, 18]. Measurements were taken over periods of ~15 min with gate times varying from τ = 1 – 10 s, and a sampling interval of T = τ + 1s. The fCEO signal was recorded after LPF1 but before the comparator (see Fig. 4(a)). To count frep, part of the signal from the PD was passed through LPF2 to remove harmonics of frep and to provide one input to a frequency mixer. The other input to the mixer was from SSG2, whose frequency was offset from frep by 20 kHz. By measuring the heterodyne output from the mixer rather than frep directly, the counter could record to a higher resolution, see Fig. 4(b). The system noise associated with the electronics and clock, felec, was measured by replacing the frep signal from the PD with SSG1 set equal to frep and recording the frequency fluctuations over the same gate times. These measurements were repeated with SSG1 set to 10 MHz and SSG2 set to the frequency offset by 2 kHz which gave similar results to felec, with fractional instabilities slightly larger than those for the Rb clock. The system measurements were repeated using a second Rb clock to reference the frequency counter (and provide one input to the mixer at 10 MHz), allowing the Rb clock to be characterized by an out-of-loop measurement with an equivalent characterization of the electronic system. This gave results nearly identical to the initial measurements, indicating that our results were limited by the stability of the Rb clock and system electronics, implying no advantage to taking out-of-loop measurements.
Fig. 4 Configurations for recording frequency data for two-sample frequency deviation calculations. (a) Direct measurement of fluctuations in the OPO signal-pulse fCEO using frequency counter. (b) Measurement of fluctuations in the Ti:sapphire frep by the heterodyne technique. SSG, synthesized signal generator; APD, avalanche photodiode; PD, photodiode; LPF, low-pass filter; Amp, amplifier.
In Fig. 5 we present time-series data for fCEO and frep for a 1s gate time. The results for fCEO showed an instability about the 10 MHz frequency lock with a standard deviation of 0.17 Hz, comparable to the value of 0.09 Hz inferred from the phase-noise measurements. As expected, the frep measurements showed lower instabilities, with a standard deviation of 6.0 mHz, compared to 6.7 mHz for felec, showing the stability measurement of frep was limited by the measurement equipment used. The two-sample frequency deviation for the CEO-frequency (ΔfCEO), repetition rate (Δfrep) and electronic system (Δfelec) used for frep stabilization were measured [19], with the fractional stability calculated [13], and plotted in Fig. 6 . The data for 100 s were calculated by averaging the results for 10 s. The 1 s dead time in each sampling interval increases the instability calculated so the results are worst-case values. The data for the Rb clock [18], are also plotted for comparison and show the overall stability limitation of the system. The two-sample frequency deviation for fCEO was calculated as 0.174 Hz and for frep was 6.1 mHz, which when scaled to the optical domain by the mode number of 714285 implied fractional stabilities of 2 x 10−11 (frep) and 1 x 10−15 (fCEO). These results are comparable with the 2 x 10−11 s instability of the Rb clock, verifying that servo-control of fCEO and frep was effective in stabilizing the comb to at least this level of precision.
Fig. 5 Frequency fluctuations from a mean value recorded on a frequency counter with a 1 s gate time. (a) In-loop measurement of the fCEO beat showing fluctuations (ΔfCEO) about the 10 MHz frequency lock. (b) In-loop measurement of the frep showing fluctuations about the 280.18 MHz frequency lock. The frep was combined in a mixer with a synthesized signal offset by 20 kHz so the fluctuations shown are for this 20 kHz mixer output signal.
Fig. 6 Fractional comb instability (scaled by fn = 200 THz and n = 714285) from in-loop frep and fCEO signals. Data for the electronic system (Δfelec/felec) and the Rb clock (ΔfClock/fClock) show the intrinsic uncertainty in the frep measurements.
5. Conclusions
We measured the stability of an OPO frequency comb centered at 1500 nm. The locked fCEO signal had a −3dB bandwidth of 15 Hz (instrument-limited) and the phase-noise PSD of fCEO and frep implied a contribution of our servo electronics to the comb-line uncertainty of 110 Hz. The two-sample frequency deviation (1s gate time) showed contributions to the comb instability from fCEO of 1 x 10−15 and from frep of 2 x 10−11, comparable to that of the Rb-clock used as a frequency reference. Our results confirm the potential of this comb for optical metrology and spectroscopy, and work is in progress to include an additional slower locking loop for frep to improve the longer term stability of the comb. In the future we plan to assess its absolute stability by comparing it to an atomic optical frequency standard.
Acknowledgments
The authors are grateful to H. Margolis for her useful discussions and thank the UK EPSRC for their support through grant EP/H000011/1. TIF acknowledges EPSRC support through a Doctoral Training Account award.
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