A cavity-enhanced absorption spectrometer was used to saturate several lines of ammonia in the 1510 nm – 1560 nm region. Analysis of power broadening of the saturated absorption feature for one of the ammonia lines yielded a dipole moment value comparable to that of the lines in the ν1+ν3 band in acetylene. Highly reproducible frequency measurements of four ammonia line centres were carried out using a frequency comb generated by a mode-locked Cr4+:YAG laser. These results demonstrate the possible application of ammonia saturated absorption lines for frequency metrology and calibration in a spectral region lacking strong absorbers. To our knowledge, this is the first frequency measurement of saturated absorption lines in ammonia at near infrared frequencies and the first reported observation of saturated absorption lines in the ν1+2ν4 band.
©2009 Optical Society of America
Although many molecular reference lines are successfully used as frequency markers across the electromagnetic spectrum, the lack of strong molecular absorbers continues to pose a challenge in the near infrared part of the spectrum. In spite of numerous efforts and studies spanning more than three decades, there are still very few identified absorbers that can be used as reliable frequency markers in the 1450–1600 nm band. The existing well-established molecular overtone transitions in acetylene [1–4], acetylene-d [5–7], two photon transitions in rubidium , and others (for example ) span only a relatively small portion of the usable near-infrared band. The recent development of optical frequency combs with outputs between 400 nm to 2000 nm [7, 10, and 11] offers a possible solution to the calibration needs at the highest accuracy level needed by national metrology laboratories. However, from the point of view of simplicity and economy, there is still a need for inexpensive and robust molecular frequency markers, providing easy calibration with uncertainties below 100 MHz.
The ammonia molecule, known to give rise to a rich spectrum of over one thousand lines between 1450 nm and 1565 nm (6900 cm-1 – 6400 cm-1) [12, 13], has been recognized as a system which can be used as a frequency reference. A significant amount of work has been directed to the study of the near-infrared absorption of ammonia primarily for remote sensing applications [14–16]. In addition, the possible application of the overtone transitions in ammonia for test and measurement applications in the fiber telecommunications wavelength range was established quite early by several groups working on the development of frequency stabilized telecom lasers [17, 18]. In these studies, Doppler broadened overtone transitions in ammonia were used to frequency stabilize diode laser sources in the 1.5 micron band. de Labachelerie and co-workers  measured the frequencies of over 70 lines with uncertainties at the level of 25 MHz or higher in the 1491 nm-1520 nm region of the spectrum. The first saturated absorption of a near-infrared transition in ammonia was reported by our group in 2006 [19, 20]. In the most recent work by Cubillas et al. , saturated absorption spectroscopy within a hollow core photonic band-gap fiber was used to saturate a few selected transitions in the ν1+ν3 band of ammonia. In their FM spectroscopy studies, the saturated absorption lines were pressure and transit-time broadened to approximately 40 MHz, and the line centers were measured with ascribed uncertainties of 12 MHz. The broadening of these lines is an intrinsic feature of the in-fiber absorption method in which a relatively high pressure (200 Pa), and small core size (20 μm) are used to obtain good signal-to-noise levels.
In the present work, we have used cavity-enhanced absorption spectroscopy to saturate several lines of ammonia, under conditions of low pressure 2.7 Pa – 4.7 Pa (20-35 mTorr) and relatively small transit time broadening. The saturated absorption line-widths were within the 1 MHz to 2.5 MHz range depending on the specific intra-cavity laser power, and the gas pressure used. We have also studied the power broadening of one of these lines at 1531.65 nm to measure the transition dipole moment. It was possible to lock the frequency of the laser system to all of the saturated absorption features observed. Finally, we have performed the frequency measurement of six lines using a known laser standard reference frequency (13C2H2 -P16) and a frequency comb generated by a mode-locked Cr4+:YAG laser which allowed the measurement of the frequency interval between the laser standard and the unknown ammonia line. Based on the results of these measurements, it is considered that four of the measured lines can be used with good utility as optical frequency references. These results together with the recent work of Cubillas and co-workers  demonstrate the potential of the rich ammonia spectrum as a source of precise frequency markers in the 1450 nm–1565 nm region of the near infrared.
2. Overview of existing ammonia near –infrared Spectroscopy
A comprehensive study of the near-IR ammonia transitions was conducted by Lundsberg-Nielsen and co-workers , who used a Fourier transform spectrometer (FTS) to record and analyze the very complex spectrum of 14NH3 between 1450nm and 1560nm. They observed a total of 1710 lines, and assigned 381 of these ro-vibrational transitions to the ν1 + ν3 N-H stretching combination band, and to the weak overtone 2ν3 band. The wave-numbers of all the transitions, with uncertainties of 0.01 cm-1 (300 MHz), and measured line-strengths were also provided. To date, the Lundsberg-Nielsen work serves as the most complete reference in the discussion of ammonia NIR absorption lines. Due to the complexity of the ammonia spectrum caused by the molecular level mixing and the resulting strong perturbations of their energy levels, a large number of NIR lines remain without proper vibrational and rotational number assignment. Furthermore, some of the original assignments proposed in  have been questioned recently . Also Xu et al. , have reported transition wave-numbers, absorption coefficients and line-widths for the ν1 + ν3 N-H stretching combination band. The energy level term values as well as spectroscopic splittings were fitted using a linear effective Hamiltonian. The same group  provided the best rotational line J and K assignments to date for many NIR ammonia transitions in the ν1 + 2ν4 band. It needs to be stressed that in the case of the ν1+2ν4 band of ammonia, the inversion splitting, as well as l-doubling energies which were determined from the term values, displayed irregularities with J and K, most likely caused by perturbations from other states. The positions of the perturbing states as well as their symmetries were not known, so a full analysis was not possible. The estimates of the principal ν1+2ν4 parameters in  were obtained from a simple single-state effective Hamiltonian. Fortunately, the lack of a full understanding of the details of ammonia structure does not preclude the usefulness of saturated absorption lines as frequency markers.
3. Description of the apparatus and observation of saturation absorption
3.1 Ammonia stabilized laser system
The ammonia-stabilized laser system is shown in Fig. 1. It has been described in greater detail elsewhere [3, 24]. The output from an external-cavity diode laser (ECDL) (New Focus model 6328H) was phase modulated at a frequency of 10 MHz using an external electro-optic modulator (EOM) and locked to a resonance in a Fabry–Perot (F–P) cavity through the Pound–Drever–Hall technique . When locked to the F–P cavity, the laser line-width was reduced to approximately 70 kHz (50 ms observation time) from a free-running line-width of 500 kHz. The F–P cavity consisted of two mirrors of equal reflectivity, one flat and one with a radius of 1 m, mounted on piezo tube linear translators at the ends of an invar spacer. The length of the cavity was 30 cm and the measured empty cavity finesse was 600. The cavity was placed in a vacuum tank which was filled with research-grade, natural NH3 (99.6% 14NH3). Saturated absorption of the NH3 lines was achieved through the increased effective path length and increased intra-cavity power afforded by performing the absorption measurements in the gas-filled resonant cavity. To stabilize the laser to the saturated absorption feature, a 1.137 kHz modulation was applied to one of the cavity piezos and the transmitted signal was demodulated at the third harmonic (3f) of the modulation frequency with a commercial lock-in amplifier. For the frequency measurements, the standard operating conditions of this system were set as follows: intra-cavity one-way power = 180 mW (52 W/cm2 one-way intra-cavity intensity near the input mirror); ammonia pressure = 4.68 Pa ± 0.13 Pa (35±1 mTorr); and modulation amplitude = 2.5 MHz, peak-to-peak.
The saturated absorption features had depths ranging from less than 0.5% to 4% of the Doppler broadened absorption peak. The observed signal to noise (S/N) ratio of the 3f demodulated signal ranged from 8 to 40 (25-Hz bandwidth) depending on the strength of the line. This experimental system allowed for variation of the input laser power and ammonia gas pressure.
3.2 Studies of the saturated absorption of ammonia
In our attempts to saturate various lines in ammonia, we were guided by results on line strengths reported in . It was not surprising that some of the lines reported by Lundsberg-Nielsen et al. as relatively strong were very difficult to saturate, as they were simply blends of many lines rather than individual lines corresponding to very strong transitions. We also found that some of the lines reported as the weakest in  yielded a very strong S/N ratio for their saturated absorption. Another reason for such pronounced differences between results reported in  and the observation of the saturation for a particular line stems from the fact that the line strength measured in linear absorption depends not only on the dipole moment but also on the population distribution  which favors transitions involving lower lying energy levels.
Figure 2(a), shows the trace of the strongest saturated absorption signal studied, obtained for a line at 1531.65 nm (tentatively identified as: ν 1+ν 3 band, K=5 ← 6 sub-band pP(6,6)-a transition ; and as line 301 in ). The saturated feature depth is approximately 4% of the Doppler broadened line. The third harmonic (3-f) demodulated (see Fig. 2(b) signal-to-noise ratio was 40 (25-Hz bandwidth) at an intracavity pressure of 2.7 Pa (20 mTorr) and power of 320 mW.
One possible concern from the point of view of using the 14NH3 lines as frequency markers in the kilohertz-precision regime, is the non-zero nuclear quadrupole moment of 14N, which gives rise to hyperfine structure for the ΔF = ±1 transitions (F=J+IN , where IN is the nuclear spin =1 for 14N). In the case of ammonia, with the quadrupole moment parameter=4.08MHz, the whole hyperfine multiplet would be located within 10 MHz of the central line. This structure has been shown to take the form of symmetric low-intensity satellites (less than 1% central line intensity for J=5 or higher) . The low intensity of these lines - below the signal to noise level achieved in our experiment - precluded us from observing them directly in transmission or in the demodulated signal. While they may still lead to a small shift of the lock point in our cavity-enhanced absorption spectrometer, the shift is expected to be approximately constant for the range of operating parameters studied. Our measurements detected no shifts in the measured optical frequencies of the lines studied for small changes in the operating parameters.
The transition dipole moment, μ12, of an absorption line is traditionally determined by measuring the Doppler broadened absorption profile of the line and using the relation between the spectral intensity, A(ω), and the magnitude of the transition dipole moment :
where ω0 is the central frequency of the line, n0 is the Loschmidt constant, Q is the state sum or partition function, E1 is the energy of the lower state, and E2 is the energy of the upper state. The saturation power is thus then typically established from the determined dipole moments as obtained from available linear absorption spectra and known spectroscopic level assignments and energies (Eq. (1)). For lines for which the full proper spectroscopic assignments and energies are incomplete, or for lines that are not fully resolved, the usual method of estimating the saturation power through Eq. (1) is unavailable. However one may obtain the saturation power from experiment in which the line broadening is measured as a function of power :
where Δωp is the broadened line-width, P is power in the cavity and Ps is the power at which the power broadening begins to saturate the total homogeneous linewidth, and Γ is the broadened half-width at half maximum (HWHM) of the line excluding power effects. In this case, Γ is partially dominated by the transit time broadening; and for the case of very slow moving absorbers and low pressures, Γ approaches the natural line half-width for a given transition. By applying the methods of , the transit-time broadened linewidth for the ammonia based system is estimated to be 300 kHz (FWHM). If the gas under observation is kept at constant low pressure and the effects of stimulated emission are neglected, one might reasonably expect that the square of the measured line-width will be a linear function of power. The measured profiles of the saturated absorption 1531.65-nm line at various intra-cavity powers were fitted using the simple Lorentzian function. The fits yielded values of the observed line-widths for various intra-cavity powers. As an example, a series of data is shown in Fig. 3. Linear regression analysis of all data yielded Γ/2π =830(30) kHz, Ps= 240(15) mW.
3.3 Evaluation of Dipole moment for NH3 from the saturated absorption.
For the case of cavity enhanced absorption, the molecules are experiencing a standing wave field and the one-way power (P) in the cavity is related to the electric field (E) by 
where w0 is the beam radius.
The condition for saturation of the transit-time broadened line is :
where μ12 is the dipole moment for a given transition and Γ is the transition line half-width (in radians/s). By combining Eqs. (3) and (4), the dipole moment μ12 can be written in terms of the saturation power Ps and linewidth Γ
Using the experimentally established values of Γ/2π = 830(30) kHz , Ps = 240(15) mW, and w0 = 0.48(4) mm, we have obtained the dipole moment of 2.5(2) × 10-32 C-m (7.4(7) mD). This result is comparable with the dipole moment value of 1.0 × 10-32 C-m for the 13C2H2 P(12) line of the ν1 + ν3 band given in . The fact that for several lines in ammonia, the dipole moments are comparable to those in acetylene shows promise for also using the ammonia lines as the reference lines in the near infrared part of the spectrum.
4. Frequency measurement of saturated absorption lines in ammonia.
In our search for suitable frequency references in ammonia, we were guided by three factors: 1) As the reference grid provided by acetylene absorption lines is quite coarse (> 70 GHz) we were interested in additional lines throughout the broader and more dense ammonia absorption spectrum; 2) Lines should be selected that possessed a sufficiently large dipole moment to allow saturation with the present intra-cavity optical powers, and 3) We were interested in lines that were well separated from neighbouring lines so they could be unambiguously identified with a commercial wave-meter with a resolution of 300 MHz and their measured linecenters were relatively unperturbed by changes in gas pressure.
Initially six candidate lines were chosen in the spectrum. Each of these was successfully observed in saturated absorption. Two of the lines initially measured in these studies were subsequently discovered to have other saturated absorption resonances in their vicinity ( 30-100 MHz) which diminished their utility from a practical point of view as they could not be resolved using a commercial wave-meter. These are lines centered at 1512.2nm (very strong line 706 according to ), and 1522.4 nm (ν1+ν3 band, K=2 ← 3 sub-band pP(3,3)-a transition ; line 453 in ). The lines for which repeated frequency measurements were performed and are reported in this work are as follows:
- 1531.65 nm ν1+ν3 band, K=5 ← 6 sub-band pP(6,6)-a transition ; line 301 in 
Measurements of the frequency for the diode laser system stabilized to a particular ammonia line were performed by measuring the frequency interval between its frequency and that of a reference laser system stabilized on a known line in acetylene. The principle of using a femtosecond Cr4+:YAG laser frequency comb for relative frequency measurements with respect to the P(16) line of 13C2H2 was described in detail in  and .
As shown in Fig. 4, the radiation from the Cr4+:YAG laser was split into two equal power beams that were combined with the radiation from the two different external cavity diode laser systems. While one of the diode lasers was always locked to the acetylene P(16) line, the other laser system was locked to an ammonia line for which the frequency was to be determined. To select parts of the frequency comb close to the diode laser wavelengths, the combined Cr4+:YAG /diode laser beams were then incident on a pair of 600 line/mm diffraction gratings and the relevant portion of diffracted radiation focused onto two InGaAs photodetectors. The appropriate beat signals were selected so a difference frequency technique could be used to cancel out common-mode noise and the carrier envelope offset (CEO) frequency fluctuations of the non-self referenced frequency comb . RF band-pass filters were used to select one laser-vs-comb heterodyne beat frequency near 340 MHz and the second laser-vs-comb beat in the 700-800 MHz range. These frequencies were chosen because of the availability of RF bandpass filters with passbands of the appropriate widths for the frequency modulated beat signals. The beat signals between the diode lasers and the comb were then amplified, and the selected beats were further band pass filtered and then mixed to yield a difference frequency signal. Finally, a tracking oscillator was locked to the mixer output, and a frequency counter was used to measure its frequency.
4.1 The acetylene stabilized system.
In this work, the reference laser system was stabilized on the P(16) line of the ν1+ν3 band in 13C2H2 . This line has been accurately measured by a number of laboratories from around the world and the uncertainties associated with realizing the frequency have been well characterized. The reference transition has also been selected by the International Committee of Weights and Measures as a reference frequency for the 1.5 μm region . The reference laser system has been described in detail in  and . An amplified external-cavity diode laser (ECDL) (New Focus model 6328) was locked to a resonance of the Fabry–Perot (F–P) cavity through the Pound–Drever–Hall technique . The components of the gas filled cavity absorption system and the stabilization circuitry were identical with the ammonia stabilized laser system. The vacuum tank was filled with research-grade, isotopically pure (> 99% purity) 13C2H2 at a pressure of 2.67 ± 0.13 Pa (20 ± 1 mTorr) .
For locking to the saturated absorption feature, a 1.137 kHz modulation was applied to one of the cavity piezos and the transmitted signal was demodulated at the third harmonic (3f ) of the modulation frequency with a commercial lock-in amplifier. The resulting signed error signal was sent to an integrating servo system (open loop unity gain at 100 Hz) that controlled the same cavity-piezo. The P(16) saturated absorption feature had a depth of 7% of the Doppler-broadened line and a FWHM of approximately 800 kHz, primarily due to transit-time and pressure broadening. A signal-to-noise ratio (S/N) of approximately 40 in a 25-Hz bandwidth was obtained for the 3f demodulated signal. In the following measurements, the acetylene stabilized system parameters were set as follows: intra-cavity one-way power = 220 mW (35 W/cm2 one-way intra-cavity intensity near the input mirror); acetylene pressure = 2.67 Pa (20 mTorr); and modulation amplitude = 1.8 MHz, (peak-to-peak). In practice, the laser system could remain locked to the acetylene transition for periods of several hours, limited by thermal drifts in the F–P cavity.
4.2 Description of the Cr4+: YAG laser frequency comb system.
The Cr4+: YAG laser system, used in the measurements of the frequency interval between the laser stabilized to the ammonia lines and the reference laser stabilized to 13C2H2 P(16), is presented schematically in Fig. 5. This system has been described in greater detail in  and . The laser cavity consists of a 1.12-m long Z-fold optical resonator comprised of flat and 10-cm radius-of-curvature concave mirrors. Stable mode-locked operation of the laser was obtained by means of a semiconductor saturable absorber mirror (SESAM) , mounted on a piezo-electric translator (PZT) at one end of the optical resonator. This arrangement allowed for reliable mode-locked operation over a period of several hours. An output power of 200 mW was obtained at a 130 MHz repetition rate. The laser provided pulses of approximately 80 fs duration (spectral FWHM=30 nm), and the centre wavelength of the laser spectrum could be shifted from 1530 nm to 1550 nm by lateral adjustment of the SESAM position with respect to the resonator optical axis. The laser spectral profile used in the ammonia measurement is presented in Fig. 6. As discussed in , the laser spectrum showed significant modulation associated with the presence of weak satellite pulses separated by several picoseconds from the main ultrashort pulse. Their presence did not prevent the mode-locked frequency comb from being used to obtain highly accurate frequency interval measurements.
To stabilize the relative frequencies of the comb, the repetition rate of the laser was controlled by means of the PZT actuator on which the SESAM was mounted. The servo-loop utilized the 10 MHz signal derived from an NRC hydrogen maser to phase-lock the repetition rate of the Cr4+: YAG resonator. The hydrogen maser absolute frequency was determined in relation to the NRC primary Cs clock reference ensemble and had an overall uncertainty of less than 3×10-14. Using this stabilization scheme, the repetition rate contribution to the frequency measurement uncertainty was negligible relative to the other uncertainties in the experiment.
4.3 Results of the frequency measurements.
The frequency difference between the unknown NH3 line frequency and the acetylene P(16) reference line is given by:
Where: (m-n) is an integer describing the order number of the comb elements, and frep and ft are the laser repetition frequency of the spanning frequency comb laser, and tracking oscillator frequency, respectively. Since the previously reported values for the frequencies of the transitions in the overtone band of NH3 were not known with great accuracy (300 MHz from , or 12 MHz from [22, 23]), the value of the integer “m-n” and the sign had to be determined from several independent measurements using well defined, but significantly different values of frep..
Typically the measurements were repeated in a series of at least three 60-second frequency counts for each repetition rate frequency. The repetition rate was then changed by several kilohertz to a different value, the acetylene and ammonia stabilized lasers were re-locked, and the frequency count was repeated. Before each set of measurements, the servos of both diode laser systems were relocked. Data were gathered for at least 3 sets of measurements with different repetition rate frequencies. Each line frequency was measured on at least two different days within a three week span. A typical heterodyne frequency beat-note S/N was 35 dB in a 100 kHz bandwidth. A tracking oscillator was locked to the beat-note and its output frequency counted for a period of 60 s with a gate period of 1 s. The standard deviation of the 1-s samples was found to be in the range of 2 to 10 kHz. Figure 7 shows the observed scatter of the measured frequency for the 1531.65-nm line as measured on four different days.
Table 1 gives the summary of all the frequency measurements and the combined standard uncertainties (in brackets). These uncertainties are calculated by combining the uncertainty due to the day-to-day repeatability of the system (see Fig. 7) with the systematic uncertainty in the frequency of the system locked to the acetylene P(16) line and the shift sensitivities of the cavity-enhanced absorption spectrometer to changes in pressure, intracavity power, and modulation amplitude. The uncertainty in the frequency of the laser locked to the acetylene P(16) line is estimated to be 2 kHz from comb-based measurements  of the absolute frequency of this laser taken over a period of several years. The shift sensitivities for the laser locked to the ammonia lines were observed to be small and could not be reliably measured. An estimate of the associated uncertainty contribution is obtained from similar work on the 12C2H2 system, as summarized in Table 1 of . By combining the uncertainty contributions due to the setting of the pressure, power, modulation amplitude, and the electronic offsets from , we obtain a conservative estimated uncertainty contribution of 2.5 kHz. The uncertainty due to the maser offset was less than 1 Hz.
In our exploratory studies, we found that saturated absorption could be achieved for many lines in the ν1+ν3 band and the weaker ν1+2ν4 band of 14NH3. Our studies of power broadening of the saturated absorption lines yielded a relatively large value of the dipole moment for NH3 absorbers in this wavelength region. A transition dipole moment value of 2.5(2)×10-32 Cm (7.4(7) mD) was found for the pP(6,6)-a ν1+ν3 band, K=5←6 sub-band line at 1531.65 nm. We have measured the frequencies of four ammonia lines in the telecom band with combined (1-σ) uncertainties of 3 to 5 kHz. The results obtained for these lines indicate that the corresponding transitions might serve as accurate frequency markers for optical metrology. In addition, these results demonstrate that other near infrared molecular transitions in ammonia may be used in future optical frequency standard studies.
We would like to acknowledge the essential technical support provided by Raymond Pelletier in the design and optimization of the electronic systems used in this work. We would also like to thank J.S. Boulanger and S. Cundy for providing and monitoring the hydrogen maser reference signals used in these studies, and Pierre Dubé for critical help in the refinement and preparation of the manuscript. Two authors (A. Czajkowski and M. Corrigan) gratefully acknowledge the support from a Natural Sciences and Engineering Research Council grant.
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