1-GHz repetition rate femtosecond OPO with stabilized offset between signal and idler frequency combs

We report an optical parametric oscillator (OPO) based on periodically poled lithium niobate (PPLN) that is synchronously pumped by a femtosecond Ti:sapphire laser at 1 GHz repetition rate. The signal output has a center wavelength of 1558 nm and its spectral bandwidth amounts to 40 nm. The OPO operates in a regime where the signaland idler frequency combs exhibit a partial overlap around 1600 nm. In this near-degeneracy region, a beat at the offset between the signal and idler frequency combs is detected. Phase-locking this beat to an external reference stabilizes the spectral envelopes of the signaland idler output. At the same time, the underlying frequency combs are stabilized relative to each other with an instability of 1.5×10−17 at 1 s gate time. © 2008 Optical Society of America OCIS codes: (190.7110) Ultrafast nonlinear optics; (190.4970) Parametric oscillators and amplifiers; (120.3940) Metrology. References and links 1. S. A. Diddams, J. C. Bergquist, S. R. Jefferts, C.W. 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Introduction
Visible continuous-wave (cw) lasers with subhertz linewidths locked to a narrow clock transition of a single trapped ion or an ensemble of laser-cooled neutral atoms produce a stable optical frequency [1], [2], [3], whose instability may ultimately reach the 10 −18 level [4]. Recently, such optical frequency standards have been reported with a fractional frequency uncertainty below 7 × 10 −17 and an instability of 4 × 10 −15 at 1 s gate time [5], [6]. Femtosecond laser frequency combs (FLFC) are a convenient means for transferring the properties of such optical frequency standards to other optical frequencies and to the microwave domain. FLFCs based on mode-locked Ti:sapphire lasers have so far shown the best performance for optical and microwave frequency synthesis relative to optical frequency standards in terms of uncertainty (8 × 10 −20 ), instability (1.8 × 10 −17 at 1 s gate time) [7] and residual linewidth (23 mHz) [8]. They are, however, not capable of reaching wavelengths beyond approximately 1200 nm, thus far precluding their use for frequency dissemination over long-distance fiber networks at telecom wavelengths. Thus currently, the 1550 nm region is mostly accessed with Erbiumdoped femtosecond (fs) fiber lasers. A relative uncertainty of 5.3 × 10 −19 [9], an instability of 6 × 10 −17 at 1 s gate time [10] and a residual linewidth of 300 mHz [11] has been reported for these sources. While this performance begins to approach that of the best Ti:sapphire systems, a unique advantage of the latter is the fact that they reach repetition rates as high as 5 GHz [12].
The highest repetition rate for a self-referenced Er fiber system is 250 MHz [13]. High repetition rates are beneficial because of a greater power per mode and the corresponding higher signal-to-noise ratio for beat signals versus cw lasers [14]. While 1550 nm mode-locked lasers at GHz repetition rates have recently become available based on Yb-Er fibers and Cr 4+ :YAG crystals, self-referencing of such sources has not yet been demonstrated, likely due to their limited peak intensity [15], [16]. Here, we pursue an alternative approach that aims at taking advantage of the unique performance of Ti:sapphire based systems by transferring their properties to the 1550 nm region using a nonlinear conversion step. To this end, we have constructed a compact femtosecond OPO operating at 1558 nm, that is synchronously pumped by a powerful Ti:sapphire femtosecond laser with 1 GHz repetition rate. While 1 GHz femtosecond OPOs have been demonstrated before at 1300 nm using pumping concepts with several pulses in the cavity [17], [18], this is the first demonstration of fundamental pumping at 1 GHz repetition rate with a single pulse in the cavity. A significant advantage of fundamental pumping is the fact that nonlinear gain is supplied upon each passage through the OPO crystal. While previous stabilization schemes for femtosecond OPOs stabilize the spectral envelope [19], [20], we introduce a method where both the spectral envelope and the underlying frequency comb of the signal and idler output are stabilized relative to each other and are absolutely stabilized if the pump laser comb is fixed. Our concept is similar to the work of Kobayashi and Torizuka performed with a femtosecond OPO at 1275 nm, where different sum frequency generation products of the pump laser and the OPO were stabilized relative to each other in order to produce phase-locked subharmonic optical pulses [21]. Our scheme recycles a large fraction of the 800 nm pump power, which could be used for producing broadband spectra covering the 500 − 1000 nm region in a nonlinear fiber. Thus, our concept may be specifically useful for bridging the gap between the visible frequencies of many local oscillators of current optical frequency standards and linking them to the 1550 nm region. In addition to possible use as an FLFC, we envision applications of this system in other spectroscopic areas such as two-color optical pump-probe experiments. Figure 1 shows the experimental setup. The Ti:sapphire based femtosecond ring laser [22] is pumped by 6.5 W of 532 nm cw light. It emits 30 fs pulses at a center wavelength of 800 nm with a repetition rate of 1 GHz and provides 1.2 W of average output power. The output pulse train is coupled into the OPO ring cavity through its output coupler OC2 (97 % transmission for 740 − 950 nm, 2 % transmission from 1430 nm to 1650 nm) and focused into a periodically poled lithium niobate (PPLN) crystal by means of the curved mirror M1. The OPO cavity is completed by the curved mirror M2 and the flat mirror M3. M1, M2 and M3 are high reflective for 750 to 850 nm and 1400 to 1625 nm. Both curved mirrors M1 and M2 have 30 mm radius of curvature, the same value as is used in the Ti:sapphire pump laser. In contrast to typical pumpcoupling schemes for OPOs [17], [18] additional pulse broadening due to a focusing lens is avoided with the present setup. At the same time, the distance travelled by the pump pulses from the Ti:sapphire crystal to the PPLN crystal approximately matches the cavity length of the pump laser and the OPO, thus ensuring that the pump pulses are focused at the center between M1 and M2, where the PPLN crystal is located. A residual mode-mismatch between the pumpand the signal beam in the PPLN crystal, due to the differing wavelengths, may be eliminated by adjusting the M1-M2 distance. The latter provides leverage on the signal beam waist when the OPO cavity is operated close to the inner edge of its stability range. The setup is particularly useful for frequency comb applications, because approximately 900 mW of residual pump light exit through OC2 and can be recycled in order to produce an octave spanning spectrum and measure the pump laser carrier-envelope offset frequency f 0,p . The 1 mm long multigrating PPLN crystal is antireflection coated for wavelengths between 750 and 850 nm and between 1500 and 1750 nm. The quasi-phase matching (QPM) period Λ can be varied from 19.5 to 21.3 μm in 0.2 μm steps. Here we used Λ = 19.9 μm. The PPLN crystal is heated to 165 • C in order to avoid photorefractive damage. For fundamental synchronous pumping the signal pulse round-trip time in the OPO cavity has to be matched to the 1 GHz pump laser repetition rate. To achieve this, the OPO ring cavity length is roughly preset to 30 cm. More precise cavity length control is enabled by using a translation stage to adjust the OC2 position and a piezoelectric transducer (PZT) supporting M3. Here, cavity length tuning [23] of the signal center wavelength is continuously feasible from 1480 to 1580 nm. The signal output power for a center wavelength at 1558 nm is 80 mW and its spectral full width at half maximum (FWHM) is 40 nm. This bandwidth supports 65 fs pulses. The OPO pump-signal conversion efficiency is approximately 8 % and the pump threshold for OPO oscillation is 710 mW. The bulk of the idler light is not resonant in the cavity and is transmitted through the cavity mirrors.

Stabilization scheme
The individual teeth of the pump-f p , signal-f s and idler-frequency combs f i are expressed as where k p,s,i are integers enumerating the comb teeth, f rep and f 0,p,s,i are the repetition rates and the carrier envelope offset frequencies of the pump-, signal-and idler-frequency combs. k s is on the order of 2 × 10 5 . The signal-and idler pulse trains have the same repetition rate f rep as the pump. The comb offset frequencies f 0,p,s,i are related to each other through energy conservation To support synchronous pumping, the signal light group-delay in the OPO cavity must at all times equal the inverse pump laser repetition rate. In order to fulfill this condition, changes of the OPO cavity length relative to the pump laser cavity length, e.g. through external perturbations, automatically cause a shift in the signal light spectral envelope λ s mediated by groupdelay dispersion: Here, ΔL is the offset between the geometrical cavity lengths of the OPO and the pump laser, L C is the length of the PPLN crystal and n g the group index of the signal pulse in the PPLN. This effect is widely used for wavelength tuning of synchronously pumped OPOs [23]. As a second condition, the signal comb teeth resonating in the OPO cavity must fulfill the standing wave condition. For an arbitrary resonant signal comb tooth this is written as where c is the mean phase velocity in the cavity and p the integer number of standing signal waves fitting into the OPO cavity. The consequence of Eqs. (3) and (4)  present experiment the OPO is operated in a nearly degenerate regime, where the signal and idler spectra exhibit a partial overlap around 1600 nm ( Fig. 2(a)  overlap region with photodiode PD1 (InGaAs p-i-n diode) a signal with a radio frequency (RF) spectrum as shown at the bottom of Fig. 3 is detected. The contribution at 1 GHz represents the repetition rate f rep . The peaks labelled f SIO and f rep − f SIO are beats between the signaland idler frequency combs (see illustration at the top of Fig. 3) that are only detectable in the overlap region of the signal-and idler spectra at around 1600 nm. The beat at f SIO represents the offset between the signal-and idler frequency combs (SIO) and is defined as Under the assumption that the repetition rate f rep and the carrier-envelope offset frequency f 0,p of the pump laser are constant, an active stabilization of f SIO via the OPO cavity length L (Eq. (4)) fixes f 0,s and f 0,i through energy conservation (Eq. (2)) and thus the positions of the signaland idler frequency combs relative to each other (illustration Fig. 3) and to the pump frequency comb. However, in the present experimental setup (Fig. 1)  A schematic of the active feedback loop used for signal frequency comb stabilization is shown in Fig. 1. The OPO output is separated from the Ti:sapphire pump light using a dichroic beamsplitter (BS 800/1558), reflecting wavelengths between 750 and 850 nm and transmitting light between 1500 and 1650 nm. Afterwards the degenerate part of the OPO spectrum is isolated from the rest using an optical bandpass filter at 1600 nm with a transmission bandwidth of 10 nm (BP 1600). After this bandpass filter approximately 10 μW of optical power were present. For the feedback loop, f SIO is isolated with a tunable RF bandpass filter (500 − 1000MHz). For an increased operating range f SIO is divided by 64 using a prescaler. The subsequent digital phase detector compares f SIO /64 with a reference frequency, obtained from a signal generator and provides an error signal. This error signal is supplied to the PZT via an adjustable loop filter and a high voltage amplifier (HVA) such that f SIO /64 is stabilized to the reference frequency.

Characterization of the stabilization
In Fig. 2(b) the signal center wavelength is shown over a period of 110 seconds for the actively stabilized and the freely oscillating OPO. In the freely running case the instability amounts to 4.3 nm, mostly caused by environmental perturbations to the OPO-and pump laser cavity length. These fluctuations are suppressed to better than 0.15 nm when the feedback loop is engaged (limited by the 0.3 nm resolution of the spectrometer). In the PPLN crystal the second harmonic (SH) of the signal frequency comb is also generated. Its spectrum partially overlaps with the Ti:sapphire pump spectrum at around 780 nm. Using energy conservation (Eq. (2)) and the definition of f SIO , the offset f 2SPO between the frequency-doubled signal comb 2 × f 0,s and the pump comb f 0,p , that can be detected at 780 nm, is expected to be Thus, a beat signal detected with PD2 (Si p-i-n diode) at 780 nm can be used for an out-of-loop characterization of the signal frequency comb stabilization at 1600 nm. For a first characteriza- tion of the signal frequency comb stabilization, the beat at the frequency f SIO was phase-locked to an external reference at 748.8 MHz. Using a vector signal analyzer, the power spectral density (PSD) of phase fluctuations S Φ ( f ) of the beat frequencies detected at 1600 nm (in-loop signal) and at 780 nm (out-of-loop signal) have been measured (see Fig. 4 for out-of-loop PSD spectrum). From these phase noise data the root-mean-square (RMS) accumulated phase jitter was numerically calculated (see plot vs. right axes in Fig. 4). For the integration limits f min = 6.25 mHz and f max = 0.5 MHz the calculation results in Φ RMS = 0.461 rad for the in-loop RF-signal and Φ RMS = 0.472 rad for the out-of-loop RF-signal. From these values we infer that the linewidth of the signal frequency comb relative to the pump frequency comb can be at the level of a few millihertz. For the Ti:sapphire pump laser FLFC, a residual linewidth of 23 mHz has been demonstrated earlier, when locked to an optical reference [8]. Under the assumption that parametric downconversion and SHG are independent processes, the frequency counting experiment also permits a test of energy conservation during these processes. While we are not aware of a theory explicitly predicting a violation of Eq. (2), processes like Raman or Brillouin scattering might in principle lead to energy depositions in the nonlinear crystal. If there were such a violation, this would cause an offset between the in-loop and the out-of-loop counter data. From an analysis of the mean values, we observe no such effect within an uncertainty of 1.22 × 10 −4 Hz. This reduces the possible error in Eq. (2) by a factor 10 9 compared to similar experiments where the precision of parametric downconversion in a femtosecond OPO was verified to be better than 200 kHz [24]. We thus conclude that energy is conserved in the combined parametric downconversion and subsequent SHG process with a fractional uncertainty of 6 × 10 −19 . Similar to previous tests of energy conservation during single-pass difference frequency generation and sum-frequency generation [25], this interpretation does not include the possibility that there may be correlated errors in both processes that cancel exactly. Finally it is mentioned, that it is also possible to actively stabilize the signal frequency comb by means of the beat frequency f 2SPO detected at 780 nm and using the beat frequency f SIO detected at 1600 nm for the out-of-loop characterization.

Conclusion and outlook
In conclusion we have demonstrated a 1 GHz repetition rate, partially degenerate femtosecond OPO generating a signal frequency comb centred at 1558 nm with a spectral full width at half maximum of 40 nm. In the partially overlapping region of the signal-and idler spectra at around 1600 nm a beat at the radio frequency f SIO was detected, which represents the offset of the signal-idler frequency combs. Phase-locking f SIO to an external reference stabilizes the signal-and idler frequency combs relative to each other (at 1 s gate time, out-of-loop Allan deviation σ y = 1.46 × 10 −17 , accumulated phase jitter Φ RMS = 0.472 rad) as well as the center wavelengths of their spectral envelopes (instability of ±0.15 nm, spectrometer resolution limited). Following this approach for a Ti:sapphire femtosecond laser frequency comb where the repetition rate f rep and the comb offset frequency f 0,p are stabilized to an optical frequency standard, it seems feasible to transfer the unique properties (uncertainty 8 × 10 −20 , instability 1.8 × 10 −17 in 1 s [7], 23 mHz optical linewidth [8]) of GHz repetition rate femtosecond Ti:sapphire lasers into the 1550 nm region. Among other things, this would potentially be useful for precision frequency dissemination over long-distance fiber networks.