111Equation Chapter 1 Section 1Atomically referenced 1-GHz optical

parametric oscillator frequency combRichard A. McCracken,* Karolis Balskus, Zhaowei Zhang, and Derryck T. ReidInstitute of Photonics and Quantum Sciences, SUPA, Heriot-Watt University, Edinburgh, EH14 4AS, UK

* r.a.mccracken@hw.ac.uk

Abstract: The visible to mid-infrared coverage of femtosecond optical parametric oscillator (OPO) frequency combs makes them attractive resources for high-resolution spectroscopy and astrophotonic spectrograph calibration. Such applications require absolute traceability and wide comb-tooth spacing, attributes which until now have remained unavailable from any single OPO frequency comb. Here, we report a 1-GHz Ti:sapphire pumped OPO comb whose repetition and offset frequencies are referenced to Rb-stabilised microwave and laser oscillators respectively. This technique simultaneously achieves fully stabilized combs from both the Ti:sapphire laser and the OPO with sub-MHz comb-tooth linewidths, multi-hour locking stability and without the need for super-continuum generation.2015 Optical Society of America OCIS codes: (120.3930) Metrological instrumentation; (140.3425) Laser stabilization; (190.4970) Parametric oscillators and amplifiers.

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1. Introduction

Frequency combs produced by high-repetition-rate lasers are becoming valuable tools in spectroscopy [1,2] and astrophotonics [3,4], as their wide mode-spacing allows the comb lines to be individually resolved. Optical parametric oscillators (OPOs, [5]) can be used to convert the often limited bandwidth of a pump laser into otherwise unreachable spectral regions [6,7], and a number of OPO frequency combs have been experimentally demonstrated [8–10]. Due to parametric energy conservation [11], stabilizing the carrier-envelope offset (CEO) frequency of the pump laser and any OPO output creates a composite frequency comb that spans all wavelengths generated by the pump and OPO [12,13].

The standard method of detecting the CEO frequency of a laser is to generate an octave-spanning supercontinuum in a photonic crystal fiber (PCF, [14]), then employ the f-to-2f self-referencing technique [15], which provides an RF beat frequency that can be used in a feedback loop. Heterodyning a visible frequency generated in the OPO via second-harmonic or sum-frequency generation (SHG, SFG) against this same pump supercontinuum provides a CEO beat frequency that can be used to stabilize the OPO [12], even without CEO stabilization of the pump laser [16]. For Ti:sapphire-pumped systems, CEO stabilization of the OPO signal pulses in this way can be limited by the need to create a pump supercontinuum containing coherent light in the blue-green region. This issue becomes particularly severe when extending OPO operation toward GHz repetition rates: the lower peak powers of the pump pulses lead to a spectrally narrower supercontinuum and require more average power to produce the necessary bandwidth, leaving less power for pumping the OPO. Conveniently, in contrast to nonlinear techniques which become more challenging at higher repetition rates, stabilizing the comb using linear optical heterodyning becomes easier as the mode spacing and power-per-mode increase.

Here we describe a Ti:sapphire-pumped 1-GHz OPO frequency comb that is fully-stabilized without using a pump supercontinuum. The pump frequency comb is locked to a Rb-stabilized external-cavity diode laser, while OPO stabilization is achieved by locking to an internal beat frequency [17,18]. Stabilization of the internal beat between the signal and idler combs in a similar OPO running at 1.56 µm has previously been reported, however without achieving a stabilized frequency comb [19].

2. Experiment

The experimental configuration is shown in Fig. 1. A Ti:sapphire laser (Gigajet, Laser Quantum) producing 30-fs pulses at 1 GHz with 1.4 W of average power was used to synchronously-pump an OPO. The OPO contained a 1.2-mm-long PPKTP crystal (Raicol Crystals) and was tunable from 1.1-1.6 µm, producing 80-fs signal pulses along with a number of parasitic SHG and SFG outputs.

2.1 Ti:sapphire comb stabilization

An interferometer was constructed in order to obtain a beat frequency between the Nth mode of the Ti:sapphire laser νN and an eternal cavity diode laser (ECDL) dither locked to the 87Rb F = 2 → F´ = 2, 3 cross-over peak near 780.2 nm, which has a theoretical absolute frequency of 384,227,981.9 MHz [20,21], denoted by νRb. A partial reflector was used to couple 95% of the pump power (1.33 W) into the OPO, with the remaining 5% (0.07 W) coupled into a 2-m length of FC/APC single-mode patch cord (Thorlabs, P3-630AR-2). The output of the Rb-ECDL was coupled into an identical fiber, with the angled input facet necessary to prevent back reflections into the laser. This configuration produced a pair of spatially mode-matched beams that were combined on a beam splitter and steered onto a diffraction grating. The diffraction grating (Thorlabs, GH25-24V) was used in a near-Littrow configuration, providing high efficiency and large angular dispersion at 780 nm. A half-wave plate in the Rb-ECDL beam was used to obtain maximum diffraction efficiency from this arm. A second half-wave plate in the Ti:sapphire beam was used for power balancing between the two arms of the interferometer. A 750-mm lens was placed at one focal length away from the diffraction grating in order to focus the overlapping beams onto the surface of an avalanche photodiode (APD1, Thorlabs APD210). A variable slit placed before the lens allowed the number of overlapping modes on the surface of APD1 to be varied.

Fig. 1. Experimental schematic of the OPO locking scheme. BS, beam-splitter; DG, diffraction grating; PR, partial reflector, WP, wave-plate.

The signal from APD1 was low-pass filtered to remove frequencies between fREP/2 and fREP

before being mixed with a signal from synthesized signal generator (SSG) which produced a frequency chosen to give a mixing output at roughly 10 MHz. This 10-MHz difference frequency was low-pass filtered before being amplified and passed into one channel of a phase frequency detector (PFD); the 10-MHz reference output from the SSG was used a reference frequency. The output from the PFD was used as the input to a proportional-integral

(PI) amplifier which provided the error signal for Ti:sapphire comb stabilization, and was used to modulate the diode current of the pump laser (Finesse Pure CEP, Laser Quantum [22]). The locked beat note between νN and νRb is shown in Fig. 2(a).

2.2 OPO CEO lockingThe OPO was tuned to a signal wavelength of 1.56 µm by coarse adjustment of the cavity length. At this signal wavelength the OPO operates near degeneracy (1.6 µm), where the signal and idler exhibit partial spectral overlap. SHG near-degenerate signal light at 800 nm was output coupled through a cavity folding mirror and focused onto APD2 (Fig. 1). The internal beat used for CEO locking arises due to a spectral overlap close to 1560 nm between the idler and the resonant signal. Internal RF beating is not limited to the nearly-degenerate case; such beats have been observed in femtosecond OPOs operating in a dual signal wavelength configuration, and are a result of the net cavity dispersion allowing independent pulses to oscillate with the same group delay but different center wavelengths [18,23].

The detected beat between the signal and idler changes at a rate four times faster than the change of the signal CEO frequency (see §3.2), so an f/8 frequency divider was used to reduce the frequency excursions to a level easily captured by our locking electronics. The beat was referenced to a 10-MHz Rb-stabilized oscillator, and locking was achieved by actuating a piezoelectric-transducer (PZT) attached to a mirror inside the OPO cavity. The locked beat is shown in Fig. 2(b).

Fig. 2. (a) Locked beat note between the Ti:sapphire laser and the Rb-ECDL (100 kHz RBW). (b) Locked OPO beat frequency measured after f/8 divider (1 kHz RBW).

3. Results and discussion

3.1 Ti:sapphire comb locking resultsThe quality of the Ti:sapphire comb lock was evaluated by measuring the phase noise power spectral density (PSD) at the output of the PFD (Fig. 3), and by counting the beat frequency over several gate times (Hameg, HM8123) and computing the Allan deviation [24] from these data (Fig. 4). The PSD plot shows a cumulative phase noise of 3.67 rad over 1 second, integrated over 1 Hz - 64 kHz (Fig. 3, red line). The primary contributions come at frequencies >10 kHz, which was the corner frequency of the PI-controller used for locking. While the theoretical locking bandwidth of the Ti:sapphire νN stabilization loop is much higher (~700 kHz [22]), the wider linewidth of the beat signal prevented locking at higher corner frequencies. There was also a strong contribution at ~7.5 kHz, which was traced to the dither frequency used for stabilization of the Rb-ECDL. For illustrative purposes, the dither frequency can be filtered out of the phase noise PSD plot already measured (Fig. 3, green line), which shows a corresponding reduction in the cumulative phase noise to 2.85 rad. While this cumulative phase noise is much larger than has been reported using self-referencing, it is not unexpected in this case. Typical external cavity laser diodes are known to provide sub-MHz linewidths, consistent with the ~750-kHz linewidth of the locking beat, measured at the -3dB point.

The calculated Allan deviation in Fig. 4 show nearly four orders of magnitude improvement in the stabilization of νN to νRb over a range of gate times. In the absence of active pump cavity-length stabilization, over longer time periods the beat frequency would drift out of the capture range of the locking electronics. This was due to slow thermal drifts in the Ti:sapphire repetition rate, which altered the positions of the comb lines relative to νRB [25]. A small portion of the Ti:sapphire beam was focused onto a fast photodiode, and the second harmonic of the repetition frequency (2 GHz) referenced to an SSG. The cavity length was stabilized using a PZT with a corner frequency of 10 Hz. Locking the pump repetition frequency improved the long-term stability of the lock to νRb, with an in-loop fractional stability of 5.7 10-15 in a 10 s gate time. Note that Allan deviation calculations average out the linewidth of the Rb transition, and so allow vN to be referenced to such excellent precision.

Despite the wider linewidth of the locking signal in comparison to super-continuum-based locking schemes such as [12], the comb lock could be maintained for many hours at a time. This condition is due to the high-quality dither lock of the ECDL, combined with the excellent passive stability of the Gigajet laser. The long-term performance is comparable to that previously observed in self-referenced systems, however the elimination of PCF from the system removes the need to use chirp-free pulses for beat detection, as well as need for high-quality fiber launch optics for optimal super-continuum generation.

Fig. 3. Phase noise power spectral density (PSD) of the locked beat frequency between νN and νRb. The strong 7.5-kHz component arises from the dither frequency used to lock the Rb-ECDL. Red and green lines indicate the calculated cumulative phase noise over a 1-s observation time.

Fig. 4. In-loop Allan deviation calculations of the locked Ti:sapphire comb and OPO CEO frequency, with fractional stabilities expressed relative to the optical carrier. Long term stability is limited by the repetition rate locking of the Ti:sapphire laser.

3.2 OPO CEO locking resultsThe internal beat used for CEO locking arises due to a spectral overlap close to 1560 nm between the idler and the resonant signal. A small cavity length variation of ΔL causes the signal CEO frequency to change by ΔfCEO. For a CEO-stabilized pump laser, as we have here, conservation of energy [11] requires the non-resonant idler CEO frequency to shift by -ΔfCEO, producing a beat frequency change of 2ΔfCEO. The second-harmonic signal / idler pulses carry twice the CEO frequency of the fundamental fields, and so a ΔL change in cavity length produces a 4ΔfCEO change in the internal beat frequency at 780 nm. This result implies a sensitivity of the detected beat frequency to cavity length changes of approximately 5 MHz nm-1, which necessitated the approach described in §2.2 to enhance the capture range of the CEO locking loop.

The in-loop phase noise PSD of the locked internal CEO frequency is shown in Fig. 5 (red). The cumulative phase noise was 1.59 rad in 1 second, integrated over 1 Hz – 64 kHz. The corner frequency of this locking loop was 3 kHz, limited by the loaded resonance of the PZT used for cavity length control in the OPO, however the practical loop bandwidth was closer to 0.5 kHz. An out-of-loop measurement of the PSD noise was performed by splitting the beat signal before the frequency divider (80-MHz when locked) and mixing with a 70-MHz RF signal to generate a new 10-MHz beat frequency. This new frequency was passed through a comparator and into a second PFD along with a second 10-MHz reference signal, generated by the same RF source as the reference signal for the locking loop. The output from this out-of-loop PFD was used to measure the PSD of the undivided signal, which is shown in Fig. 5 (blue), after a scaling consideration that accounts for the divider used for locking [26,27]. The out-of-loop noise data presented in Fig. 5 represent a worst-case scenario for the locking stability of the OPO, as there is also a noise contribution from the Rb-locked Ti:sapphire comb. The measured value of 3.4 rad can be considered as an upper limit on the phase noise of the OPO frequency comb.

Allan deviation calculations of the locked, frequency divided internal CEO frequency are shown black in Fig. 4 and indicate a stable lock with a fractional stability slightly higher than that reported for a conventionally-locked 333 MHz OPO [10]. However, the frequency division method of increasing the capture range of the locking signal allowed excellent long term stability to be obtained.

Fig. 5. In-loop (red, lower black line) and out-of-loop (blue, upper black line) phase noise PSD measurements of the locked OPO internal beat frequency.

4. Summary and conclusions

We have described here a linear stabilization approach which addresses the limitations encountered at high repetition rates of the conventional OPO comb locking using OPO : pump-supercontinuum heterodyning. The results presented indicate that direct comb stabilization to an optical standard is very promising, and should be increasingly attractive as the pump laser repetition rate is increased even further. The 1-GHz OPO comb referenced to

a Rb-ECDL remained locked over periods of up to several hours. While the absolute noise level was poorer than can be achieved using a super-continuum lock—reflecting the limitations due to the MHz-level linewidth of the ECDL used as the optical reference and the change in comb dynamics resulting from a fixed-point lock [25]—the comb stability demonstrated is more than sufficient for many spectroscopic applications. With low-finesse filtering using a Fabry-Pérot cavity, which can be directly stabilized to the comb itself, multi-GHz mode spacing should be easily achievable.

AcknowledgmentsThis research was carried out under the METROCOMB project, which has received funding from the European Community’s Seventh Framework Programme (FP7/2007-2013) under Grant Agreement no. 605057. The authors are also grateful for funding from the Science and Technology Facilities Council (STFC ST/L002140/1).