1-GHz harmonically pumped femtosecond optical parametric oscillator frequency comb

K. Balskus,1 S. M. Leitch,1 Z. Zhang,1 R. A. McCracken,1 and D. T. Reid1

1Institute of Photonics and Quantum Sciences, SUPA, Heriot-Watt University, Edinburgh, EH14 4AS, UK*kb202@hw.ac.uk

Abstract: We present the first example of a femtosecond optical parametric oscillator frequency comb harmonically-pumped by a 333-MHz Ti:sapphire laser to achieve a stabilized signal comb at 1-GHz mode spacing in the 1.1–1.6-µm wavelength band. Simultaneous locking of the comb carrier-envelope-offset and repetition frequencies is achieved with uncertainties over 1 s of 0.27 Hz and 5 mHz respectively, which are comparable with those of 0.27 Hz and 1.5 mHz achieved for 333-MHz fundamental pumping. The phase-noise power-spectral density of the CEO frequency integrated from 1 Hz–64 kHz was 2.8 rad for the harmonic comb, 1.0 rad greater than for fundamental pumping. The results show that harmonic operation does not substantially compromise the frequency-stability of the comb, which is shown to be limited only by the Rb atomic frequency reference used.2014 Optical Society of America OCIS codes: (320.7110) Ultrafast nonlinear optics; (190.4970) Parametric oscillators and amplifiers; (140.3425) Laser stabilization; (120.3930) Metrological instrumentation.

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1. Introduction

Tunable frequency combs [1]–[4] with a wide mode spacing are in demand for astronomical spectrograph calibration [5], optical arbitrary waveform generation [6], direct comb spectroscopy [7], microwave frequency generation [8] and optical coherence tomography [9]. Combs with 1-GHz or greater mode spacing have been achieved by Fabry-Pérot filtering the modes of a lower repetition frequency comb [10, 11], by implementing a phase-matched nonlinear fiber seeded by the modulated optical carrier [12] or by using micro-resonators [13–15], however these approaches can lack tunability and often require additional electronic and mechanical locking loops to achieve useful stability.

An alternative to reach GHz frequencies is to harmonically pump an optical parametric oscillator (OPO), which can offer broad wavelength coverage [16], short pulse durations [17] and can be locked to produce low-noise frequency combs [18, 19]. Synchronously pumping an OPO limits its repetition rate to that of its pump laser, but it is possible to operate the OPO at a harmonic of this when the OPO cavity length is an integer [20, 21] or integer fraction[22, 23] of the pump cavity length. Here, we demonstrate the first example of a fully stabilized frequency comb from a harmonically pumped 1-GHz OPO.

2. Experiment

Harmonic operation is described by LOPO = nLPUMP/Q ,where L represents the pump and OPO cavity lengths, Q and n are positive integers, and n/Q is a non-divisible fraction. The relation describes an OPO cavity with n independent circulating pulses interleaved to form a pulse sequence of a repetition rate Q times that of the pump. When n = Q = 1, exactly synchronous pumping is obtained. For n = 1 and Q ≠ 1 the OPO cavity length is Q times shorter than the pump laser and the signal pulses transit the cavity Q times before interacting with the next pump pulse [23, 24]. When n ≠ 1 each set of pulses grows independently from noise, leading

to a random relative phase between each sequence, which is undesirable for frequency comb generation. For this study we utilized the short-cavity configuration with Q = 3 and n = 1.

The experimental configuration is shown in Fig. 1. A Ti:sapphire pump laser (Gigajet, Laser Quantum) produced 30-fs pulses with 1.45-W average power centered at 800 nm with a full-width half-maximum (FWHM) bandwidth of 32 nm and a repetition rate of 333 MHz. A 90% reflector was used to steer 1.3 W of pump power into the OPO, with the remaining 10% coupled into a photonic crystal fiber (PCF) for supercontinuum generation.

Fig. 1. Stabilization layout and (inset) cavities of fundamental / harmonically-pumped OPO combs. OC, output coupler; M, dielectric mirrors; PCF, photonic crystal fiber, BS, beam splitter; BPS, polarizing beam splitter; IF, interference filter; PL, polarizer; L, focusing lenses; PHD, photodiode; APD, avalanche photodiode; LPF, low pass filter; PFD; phase-frequency detector; BPF, bandpass filter; PZT, piezo-transducer; SSG, synthesized signal generator.

The 4-mirror ring OPOs (Fig. 1, inset) were based on a 1.2-mm-long periodically poled potassium titanyl phosphate (PPKTP) crystal (Raicol Crystals), which was antireflection (AR) coated at both the pump and signal wavelengths. In the fundamental 333-MHz configuration the OPO operated with a threshold of 250 mW and was cavity length tunable from 1100 to 1600 nm in the signal (Fig. 2(a)). Harmonic operation was implemented by reducing the cavity length to 1/3 of the pump laser, producing a 1-GHz output. For fundamental pumping the OPO was configured with -75-mm radius-of-curvature focusing mirrors, while for harmonic pumping this value was reduced to -32-mm to provide equivalent intracavity spatial mode conditions. The mirror coatings used in both cases were identical. The threshold at 1 GHz increased to 500 mW due to the increased losses from multiple cavity round trips, however the OPO tuning performance remained comparable (Fig. 2(b)). Both OPO configurations produced pulses with durations of 60–90 fs across the tuning range, depending on the cavity dispersion.

Fig. 2. Signal spectra from cavity-length tuning of the (a) 333-MHz and (b) 1-GHz harmonic OPO.

The pump repetition rate (fREP) was sampled with photodiode (PHD) and its sixth harmonic (2 GHz) isolated with a bandpass filter (BPF) then mixed with a 2-GHz reference

(fREP(REF)) from a synthesized signal generator (SSG1). The low-pass-filtered error signal from the mixer enters the proportional-integral (P-I) controller, generating a control signal which is used to actuate PZT1 in the Ti:sapphire laser. The repetition rate remained locked for ~2 hours without adjustments.

Carrier-envelope offset (CEO) frequency stabilization of the OPO signal pulses was implemented by heterodyning light from the pump supercontinuum with non-phasematched pump-signal sum-frequency light from the OPO, as described in [25]. The CEO frequency, fCEO, was filtered, amplified and passed through a comparator to provide an input to one channel of the phase-frequency detector (PFD) [26]. The 10-MHz clock output from SSG1 was used as the CEO reference frequency and served as the second PFD input. The PFD output provided an error signal to a second P-I controller, the output of which was connected to PZT2 in the OPO cavity to control fCEO. The OPO wavelength and fCEO could be manually tuned using a long-travel PZT stage, allowing the fCEO to be brought into the locking-loop capture range.

A frequency counter recorded instabilities in the locked fREP and fCEO over different gate times, and their Allan variance was calculated. A 10-MHz Rb clock [27] provided a common reference to SSG1, SSG2 and the counter (Fig. 3). The fCEO signal after low pass filter (LPF1) was split to sample its fluctuations and simultaneously lock it to the 10-MHz reference frequency. For the fREP stability measurements a BPF was used to remove all 333 MHz or 1 GHz harmonics (depending on the OPO configuration), and provided one input for the frequency mixer. The other frequency from SSG2 into the mixer was introduced with a 2 kHz offset to enable counting at high resolution (see Fig.3(b)).

Fig. 3. Configuration for recording frequency stability data for (a) fCEO and (b) fREP.

3. Results and discussion

First we present frequency stability measurements of fCEO and fREP for a 1-second gate time. The Allan variance in fCEO when locked to 10 MHz was close to 0.27 Hz for both the fundamental and harmonic OPOs (see Fig. 4(a,b)). This result is comparable to the value of 0.17 Hz for a 280-MHz OPO reported by Ferreiro et al [25].

The measured instabilities in fREP were 1.5 mHz and 5 mHz for the 333-MHz and 1-GHz harmonic OPO respectively (Fig. 4(c,d)). The noise limit of the locking loop was measured by replacing the photodiode in Fig 3b with a synthesized fREP signal from SSG1. The resulting frequency fluctuations implied a 5 10-12 fractional instability for a 1-second gate time, limited by the noise of the Rb clock. Measured instabilities of the Rb-referenced synthesized frequencies at 333 MHz and 1 GHz were 1.5 mHz and 4.5 mHz respectively, confirming that the stability of the OPO repetition frequency was limited by the clock source. The repetition rate instability of the harmonically pumped OPO increases proportionally with fREP due to an increase in the fractional change in cavity length of the OPO relative to the pump laser.

The fCEO and fREP fractional frequency comb instabilities for different gate times are presented in Fig. 5. The fractional stability data for the Rb clock are also plotted for comparison. The fractional instability of the locked fCEO for both OPOs over a 1-second gate was 1.35 10-15. The fractional instability in fREP over a 1-second gate time was 4.5 10-12

for 333-MHz OPO and 5.0 10-12 for the 1-GHz harmonic OPO. These results demonstrate that the frequency stability obtainable from a harmonically pumped OPO frequency comb is comparable with that from a fundamentally pumped OPO, despite the signal pulses making multiple round trips of the OPO cavity, which might be expected to enhance the contribution of environmental effects to the repetition-rate phase noise.

Fig. 4 CEO frequency instability measurements around 10 MHz over a 1-second gate time for the (a) 333-MHz and (b) 1-GHz OPO. Repetition frequency instability measurements over a 1-s gate time for the (c) 333-MHz and (d) 1-GHz harmonic OPO.

Fig. 5. Fractional frequency comb stability from in-loop fREP and fCEO signals. The data for the Rb clock show the limiting instability in the fREP locking. Frequency comb instability is shown for: (a) the 333-MHz OPO (fn = 200 THz, n = 600000) and (b) the 1-GHz harmonic OPO (fn = 200 THz, n = 200000).

The RF spectrum of the 1-GHz harmonically pumped OPO stabilized fCEO frequency was recorded using a 400-Hz span and 10-Hz resolution, showing an instrument limited bandwidth of 10 Hz at the 3 dB level (Fig. 6), which is comparable to the performance reported in[25]. In-loop phase-noise measurements of fCEO were carried out when fREP was locked by acquiring the PFD output signal with a 12-bit DAQ card. The power spectral density (PSD) phase-noise

plots for the fundamental and harmonic OPOs are shown in Fig 7. The integrated phase noise from 1 Hz–64 kHz was 1.8 rad and 2.8 rad for the 333-MHz and 1-GHz harmonically-pumped OPOs respectively. Both PSD plots show increased phase noise in the 25–32 kHz range, which arises from 27.5 kHz intensity fluctuations in the pump laser. These fluctuations couple into the Ti:sapphire laser as RIN and into the OPO as both RIN and phase noise  [28]. Noise above 1 kHz lies outside our locking loop bandwidth, which is limited by the response of the fast PZT in the OPO cavity (PZT2). If the pump noise could be reduced then the fCEO PSD for the 333 MHz OPO would be comparable to previously published results [25].

Fig. 6. RF spectrum of the locked fCEO signal recorded with a 10-Hz resolution bandwidth. The measured bandwidth was instrument limited to 10 Hz at the -3 dB level.

Fig. 7 (a) In loop 1-second observation time of the phase-noise PSD for f CEO of the (a) 333-MHz and (b) 1-GHz harmonically-pumped OPO, for which the cumulative phase noise values from 1 Hz – 64 kHz are 1.8 rad and 2.8 rad respectively.

4. Summary and conclusions

Our results demonstrate for the first time a femtosecond OPO frequency comb exploiting harmonic pumping [20–23] to multiply its repetition frequency by a factor of three (1 GHz) compared to that of its Ti:sapphire pump laser (333 MHz). Allan variance measurements of the fully phase-stabilized signal pulses from both the fundamentally-pumped and harmonically-pumped OPOs show that the use of harmonic pumping does not substantially degrade the frequency stability of the comb. The integrated phase-noise (1 Hz–64 kHz) of the CEO frequency increased by around 1 rad under harmonic pumping, with the increase arising in the 300–1000-Hz band associated with acoustic-noise contributions to the resonator stability, which couples directly to fCEO in a femtosecond OPO. Extension of this technique to higher repetition rates should be possible by using cavities with higher values of Q.

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.