High-coherence mid-infrared frequency comb

We report on the generation of a frequency comb around 4330 nm with an unprecedented coherence of the single teeth. Generating the comb within a Ti:sapphire laser cavity by a difference-frequency process and using a phase-lock scheme based on direct digital synthesis, we achieve a tooth linewidth of 2.0 kHz in a 1-s timescale (750 Hz in 20 ms). The generated per-tooth power of 1 μW ranks this comb among the best ever realized in the mid-infrared in terms of power spectral density. © 2013 Optical Society of America OCIS codes: (140.3070) Infrared and far-infrared lasers; (140.4050) Mode-locked lasers; (190.4223) Nonlinear wave mixing. References and links 1. T. Udem, J. Reichert, R. Holzwarth, and T. W. Hänsch, “Absolute optical frequency measurement of the cesium D1 line with a mode-locked laser,” Phys. Rev. Lett. 82, 3568–3571 (1999). 2. T. Udem, J. Reichert, R. Holzwarth, and T. W. Hänsch, “Accurate measurement of large optical frequency differences with a mode-locked laser,” Opt. 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Introduction
The optical frequency comb synthesizer (OFCS) is nowadays a well established milestone for visible/near-infrared metrology [1][2][3][4].Such a device has already found widespread application both as phase/frequency reference, thanks to its absolute traceability, and as source, thanks to its simultaneous broadband coverage and high coherence, providing unprecedented resolution, precision and sensitivity for spectroscopy [5][6][7].
The interest in using OFCSs in the mid-infrared (MIR) region is related to applications such as trace-gas sensing with high-finesse cavities [8], high-precision spectroscopy and frequency metrology [9].Indeed the MIR spectral range, also called molecular fingerprint region, is particularly well suited for observing most simple molecules of atmospheric and astrophysical interest, having their strongest ro-vibrational transitions that fall in this spectral region.Modelocked lasers have not yet been developed in the MIR.Multimode quantum cascade lasers (QCLs) have been proposed as direct comb sources in the MIR [10], but coherence performances similar to OFCSs have to be proven yet.Another very recent approach, developing at a fast pace, is the generation of combs in toroidal microresonators by parametric oscillation [9,11].A well established approach to generate OFCS-referenced MIR radiation is non-linear frequency conversion, in order to link this spectral region to the one where OFCSs operate.Widely tunable, narrow-linewidth OFCS-assisted continuous wave (CW) MIR sources, obtained by mixing two OFCS-locked CW NIR lasers, have been recently reported [12,13].Relatively high-power CW MIR sources have been obtained by using intracavity difference frequency generation (DFG) [14], optical parametric oscillators (OPOs) [15][16][17], and OFCSreferenced QCLs [18,19].Alternatively, sum frequency generation has been used to up-convert QCL radiation to be compared with the OFCS in the near-infrared (NIR) region [20,21].Another possibility consists in directly transferring the OFCS spectrum to the MIR region (MIRcomb).Actually, a hybrid DFG-MIR-comb, mixing a CW NIR fiber laser with an amplified NIR fiber-based OFCS, was one of the first demonstrations of direct MIR-comb generation [22] that proved also useful for phase locking other MIR sources.For applications like direct comb spectroscopy, where a higher power spectral density is needed, MIR-combs were developed using OPO generation [15,16] or DFG systems using intense fiber-based NIR OFCSs [23][24][25].
For MIR-combs, values for total and per-tooth powers of 1.5 W and 30 μW respectively, have been achieved [15].In terms of spectral purity, the best reported values for the teeth linewidth are 30-40 kHz in a 1-2-s timescale [15,24].However, frequency down-conversion of combs from the NIR to the MIR may sometimes severely degrade the coherence [26].
In this Letter we present a scheme for generating a highly coherent MIR-comb through an intracavity DFG process [14].The 1040-nm portion of the spectrum of a visible/NIR OFCS (NIR-comb) is amplified in an Yb-doped fiber and then mixed with the intracavity radiation of a Ti:sapphire (Ti:Sa) laser in a MgO:PPLN non-linear crystal.A MIR-comb centered around 4330 nm is thus generated.We demonstrate that excess frequency noise of the NIR-comb can be efficiently removed in the downconverted one by properly using a direct digital synthesis (DDS) scheme.This leads to a 2.0 kHz tooth linewidth (in a 1-s timescale) of the generated MIR-comb.In addition, the high repetition rate ( f r = 1 GHz) and the intracavity power-boosted DFG determine an average per-tooth power of 1 μW and thus a power spectral density at the μW/kHz level, comparable to the best results achieved with OPO-based MIR-combs.

Experimental setup
In Fig. 1 the experimental setup is reported.The setup is similar to that described in our work on intracavity DFG [14], based on a mode-locked Ti:Sa laser with a repetition rate f r of about 1 GHz, spectrally broadened to one octave operation range (500-1100 nm) by a photonic crystal fiber (NIR-comb).The oscillator controlling f r is referenced to a Rb/GPS-disciplined 10-MHz quartz clock with a stability of 6 × 10 −13 at 1 s and an accuracy of 2 × 10 −12 .The portion of the NIR-comb spectrum above 1 μm wavelength is selected by a dichroic mirror and sent to an Yb 3+ fiber amplifier: the output radiation, whose spectrum is limited by the amplifier gain bandwidth [Fig.2], is injected into the Ti:Sa laser cavity by another dichroic mirror.The amplifier output is used as signal in a MgO:PPLN multiperiod crystal to generate idler radiation (MIR-comb), where the pump is the intracavity Ti:Sa radiation.The MIR-comb radiation is extracted from the cavity taking advantage of different refraction angles at the facet of the crystal, cut at Brewster angle for the pump.The Ti:Sa laser is optically injected by an external-cavity diode laser (ECDL) in order to make it unidirectional and single frequency.To keep the optical injection, the Ti:Sa cavity length is stabilized against the ECDL frequency by an electronic control loop based on the polarization-based Hänsch-Couillaud technique [27]; the feedback signal is sent to a piezoelectric acting on one of the cavity mirrors.The ECDL wavelength is set to 838.5 nm in order to obtain a MIR-comb centered around 4330 nm with a signal at 1040 nm, in coincidence with the most intense portion of the amplified NIR-comb [Fig.2].The DFG scheme, considering the 838-863 nm tuning range of the pump laser injecting source  (ECDL) and the 1032-1045-nm-wide spectrum of the signal (NIR-comb spectrum after the amplifier), provides a tunability of the MIR central wavelength from 4.2 to 5.0 μm.The crystal temperature and, eventually, the period, need to be accordingly varied in order to ensure the quasi-phase-matching condition.The tuning limits for the central wavelength are given by the edges of the ECDL tuning range and the NIR-comb spectrum.Actually, the upper limit at around 5.0 μm is imposed by the absorption of the PPLN crystal.The MIR-comb spectrum is limited by the PPLN crystal phase-matching bandwidth, which is 27-nm wide FWHM at 4330 nm.This means that the portion of the NIR-comb spectrum effectively involved in the MIR-comb generation is 1.6-nm wide (see Fig. 2).With a 5 W total power out from the amplifier and 30 W Ti:Sa intracavity power, the obtained power of the MIR-comb is 0.5 mW.
Considering such an idler power, the pump radiation is reduced by 2.5 mW (the pump photons are 5 times more energetic than the idler ones); this value is negligible with respect to the total intracavity pump power (30 W), so the losses related to the DFG process are negligible [14].
In order to have a MIR-comb with narrow-linewidth teeth, the excess noise of the NIRcomb due to repetition rate fluctuations (N s × f r , with N s order number of one of the downconverted NIR teeth) must be replicated by the pump frequency, to be canceled by difference.An intermediate stable oscillator operating around signal frequencies (a Nd:YAG laser) and a DDS electronic scheme similar to that described in [13,14] are used to that purpose.ECDL and Nd:YAG frequencies (ν p and ν Y respectively) are beaten with the NIR-comb nearest teeth and the beat note frequencies are where f p and f Y are the beat note frequencies of the ECDL and the Nd:YAG respectively, f r and f o are the repetition rate and the carrier envelope offset of the NIR-comb respectively, and N x is the integer identifying the tooth used for the beat note.f o is canceled from f Y using standard RF mixing, then the DDS multiplies f Y + f o by a factor (N p − N s )/N Y .A phase-locked loop (PPL2) is used to control the pump beat-note f p against the DDS output with a large bandwidth (2 MHz).In these conditions f p = ( f Y + f o )(N p − N s )/N Y and using eq.( 1) and ( 2) the pump frequency can be written as and the frequency of the MIR-comb tooth (idler) obtained as difference between the pump laser and the signal NIR-comb tooth results It is worth noting that an absolute frequency traceability of the generated ν i is obtained by controlling the frequency of the Nd:YAG laser against the nearest tooth of the NIR-comb: a PLL (PLL1 in Fig. 1) with a bandwidth of 10 Hz corrects for Nd:YAG frequency drifts, without perturbing its linewidth.Moreover, from eq. ( 4) we note that the frequency fluctuations of ν i depends only on ν Y and are independent from NIR-comb parameters ( f r and f o ), giving narrow MIR-comb teeth.The factor (N p − N s )/N Y is about 1/4 in our case and, considering a Nd:YAG laser linewidth of about 5 kHz in a 1-s timescale, a linewidth of about 1 kHz of the MIR-comb N s teeth is expected.It is important to observe that a perfect cancellation of f r can only be obtained for the tooth N s , whereas, for the tooth N s + m (m is the integer that enumerates the MIR-comb teeth), the additional fluctuations amount to m × δ f r .The fluctuations for a generic MIR-comb tooth can be expressed as In our case the two terms are of the same order of magnitude, thus contributing to the noise at the same level (see the next section).
The MIR-comb beam is coupled to a high-finesse cavity to study the frequency noise power spectral density (FNPSD) and beaten with a previously frequency calibrated QCL at 4.33 μm in order to characterize its frequency components.A sequence of beat-notes spaced by 1 GHz are measured as the QCL frequency is scanned.This confirms the value of the center wavelength emission of the generated MIR-comb and the value of f r as expected, otherwise difficult to measure due to the lack of fast photodetectors in the MIR region.

The MIR-comb teeth
The 1-m-long high-finesse cavity (free spectral range FSR = 150 MHz) is made of two planoconcave ZnSe mirrors, with high-reflectivity coatings on the concave surfaces (6 m radius of curvature) [13].At this wavelength (4.33 μm) the finesse is 8000.To maximize the transmitted signal we have matched f r with the following Vernier ratio [28]: which corresponds to a given cavity length L 0 .In this condition, the cavity selects a subset of comb teeth (one every three), that gives rise to the peak shown in Fig. 3 where M tot is the total number of the MIR-comb teeth.Eq. ( 7) allows to estimate M tot .As an example, the measured width of the third peak is W pk = 630 kHz FWHM.Since in this case a total teeth number M tot = 440 is obtained.Calculations on the other peaks give consistent results that, recalling the total comb power, allow to estimate an average per-tooth power of 1 μW.This is also in agreement with the expected spectral coverage of the MIR-comb retrieved by the phase-matching bandwidth of the DFG process at this wavelength.Figure 3(a) also shows the effect of the phase lock technique on the width of the MIRcomb teeth.The width of the black peak, corresponding to the locking scheme described above (with DDS implemented for the ECDL phase lock), is 30 kHz FWHM, limited both by the cavity mode and by the dispersion of the teeth due to the cavity mirrors.On the other hand, the red peak, corresponding to a standard phase lock of the ECDL to the nearest NIR-comb tooth (without DDS), is much wider (about 400 kHz FWHM), confirming that the DDS really provides a narrower MIR-comb teeth, as will be discussed in the next section.

MIR-comb coherence
In order to estimate the coherence of the MIR-comb we have used the high-finesse cavity as frequency-to-amplitude converter to retrieve the FNPSD of the radiation in the condition established by eq. ( 6).The factor used to convert amplitude fluctuations to frequency fluctuations is the slope of the first peak of Fig. 3 at half maximum.Due to the photons average lifetime in the cavity, the latter acts as a second order low-pass filter with a 9.4 kHz cutoff frequency.The spectrum reported in Fig. 4 is compensated for this cutoff.Using Elliott's formula to calculate Fig. 4. FNPSD related to the MIR-comb radiation retrieved by using the high-finesse cavity as frequency-to-amplitude converter.The spectrum analyzer was set in max-hold acquisition mode to be sure to collect the maximum amplitude for each frequency interval.The spectrum is compensated for the 9.4 kHz cavity cutoff.Inset: profiles of the MIR-comb power spectrum in different timescales, calculated using Elliott's formula [29].
the linewidth of the comb teeth [29], we obtain a value of 2.0 kHz FWHM in a 1-s timescale and 750 Hz in a 20-ms timescale.This is to our knowledge the narrowest measured linewidth of a MIR-comb.Taking into account the MIR-comb power, we calculate a per-tooth power spectral density of 0.5 μW/kHz (in a 1-s timescale), which is comparable with the best values obtained with OPO-based MIR-combs [15,16].It is worth noting that this power level is in a range suitable for direct comb spectroscopy in this spectral region.

Conclusion
In conclusion we have demonstrated a highly coherent MIR-comb centered around 4.33 μm, with a tooth linewidth of 2.0 kHz and 750 Hz in a timescale of 1 s and 20 ms, respectively.An average power of 1 μW for each single tooth was achieved, which means a per-tooth power spectral density of 0.5 μW/kHz (in a 1-s timescale).The generated spectrum spans 27 nm, with a center wavelength tunable from 4.2 to 5.0 μm.The combination of such unprecedented spectral features enables particularly demanding applications, including its use as broadband MIR source for direct comb spectroscopy [30] or for manipulation of cold molecular samples, which exhibit transition linewidths below 1 kHz [31].

Fig. 1 .
Fig. 1.Experimental setup: an Yb fiber amplifier (FA) is seeded by the NIR portion of the spectrum of the NIR-comb.The amplifier output is used as signal in a MgO:PPLN multiperiod crystal to generate MIR radiation, where the pump is the Ti:Sa intracavity radiation.The MIR-comb beam is coupled into a high-finesse cavity and beaten with a room temperature distributed feedback quantum cascade laser (DFB-QCL) for characterization purposes.PLL: phase-locked loop, DDS: direct digital synthesis, APD: avalanche photodiode, BSp: beam splitter, PZT: piezoelectric transducer, DM: dichroic mirror, MgO:PPLN: periodically poled lithium niobate crystal doped with magnesium oxide, GM: gold mirror, OC: output coupler, Pol.det.: polarization detection and electronic control loop, BSt: beam stopper, M: mirror, SM: spherical mirror, L: lens, Ti:Sa: titanium sapphire crystal, PD: photovoltaic detector.
(a) (the first peak of Fig. 3(b)).While keeping f r constant, if the cavity length L is changed, other resonances can

Fig. 3 .
Fig. 3. Transmission peaks of the high-finesse cavity recorded for different cavity detunings.a) The peak corresponding to eq. (6), recorded in two different ECDL phase lock schemes: with DDS implemented (black line, 30 kHz FWHM), and with simple phase lock to the nearest NIR-comb tooh (red line, 400 kHz FWHM).b) 1-FSR-wide cavity scan (inset) with zooms on consecutive longitudinal resonances spaced by FSR/3 = 50 MHz.