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We present a novel scheme of frequency scan and wavelength modulation of a difference-frequency-generation source for comb-referenced sensitive spectroscopy. While the pump and signal frequencies are phase-locked to an optical frequency comb (OFC), the offset frequency between the signal wave and the nearest comb tooth is modulated to apply a wavelength-modulation technique, and the idler wave frequency is repeatedly swept for signal accumulation by changing the repetition frequency of the OFC. The spectrometer is applied to absolute frequency measurement of weak hyperfine-resolved rovibration transitions of the ν1 band of CH3I, and the uncertainty in frequency determination is reduced by one order of magnitude in compared with that of the previous work published in Optics Express 20, 9178-9186 (2012).
©2013 Optical Society of America
1. Introduction
Sub-Doppler resolution molecular spectroscopy in the mid-infrared region has made remarkable progress due to the development of tunable and intense sources with a narrow spectral width (e.g., difference-frequency-generation (DFG) [1–7], quantum cascade lasers [8–10], and optical parametric oscillators (OPOs) [11–14]). Some spectrometers have been combined with an optical frequency comb (OFC) to measure and/or control the source frequency with an uncertainty corresponding to a fraction of the spectral width of the Lamb dips.
We have developed a 3.4-μm DFG source and a cavity-enhanced absorption cell (CEAC) for sub-Doppler resolution spectroscopy with high sensitivity and a wide tunable range [3, 4, 6, 7, 15]. Introduction of a 1.5-μm erbium-doped fiber optical frequency comb reduces uncertainties in determining of the transition frequency [7]. These features enabled us to reduce the uncertainties of the previous frequency list of the v3 band methane transitions by more than two orders of magnitude [7, 15]. In those measurements, the idler frequency is stabilized to the Lamb dip of a particular transition, and then the pump and signal frequencies are measured using the OFC. However, this method is not applicable to transitions whose Lamb dips are too weak as frequency references to stabilize the DFG frequency.
In this study, we have developed a novel scheme of sensitive sub-Doppler resolution spectroscopy suitable for frequency determination of weak transitions. The pump and signal frequencies are phase-locked to the nearest comb teeth of the spectrally broadened OFC. The repetition frequency, which is usually stabilized at a fixed value in frequency measurements, is swept in the present work, and thereby the DFG frequency is scanned to record the spectrum. No servo control of the carrier-envelope-offset frequency is required for the DFG sources. The frequency axis of the recorded spectrum is calibrated with a relative uncertainty of the 10−12 level against a frequency base linked to the Temps Atomique International (TAI). The sensitivity of the spectrometer is enhanced by accumulating spectra over repetitive frequency sweeps without any frequency drift. To further enhance the sensitivity we perform wavelength-modulation spectroscopy, which has often been employed to extract spectral lines from noise. Indeed, Okubo et al. [6] recorded the wavelength-modulation spectrum of the ν1 band of CH3I and measured the frequency separations between hyperfine components. Ricciardi et al. [12] also carried out wavelength-modulation spectroscopy of the same band using the comb-referenced OPO and signal accumulations over the repetitive frequency sweeps and determined the absolute frequency of the centroid of the P(18,3) transition with an uncertainty of 50 kHz.
We have applied a novel scheme to the absolute frequency measurement of the ν1 band hyperfine-resolved P(22, 6) and P(23,5) transitions of CH3I. The observed spectral line is one third the width that in the previous work [12], and the uncertainty in frequency determination is 5 kHz. This scheme was also applied to the forbidden transitions of CH4 with a brief description of the experimental setup [15]. The present paper describes the details.
2. Frequency-comb-referenced DFG source and wavelength modulation
The DFG frequency is given by
where fpump is the pump frequency and fsignal is the signal frequency. They are offset-locked to the nearest individual comb mode and expressed asandwhere ni (i = pump, signal) is the mode number, frep is the repetition frequency, fCEO is the carrier envelope offset frequency of the OFC, and Δ fi (i = pump, signal) is the signed offset-lock frequency. Accordingly, the DFG frequency is derived aswhich is independent of fCEO. The difference between mode numbers is typically 1.32 × 106 in the present work. When frep is varied, the DFG frequency is swept accordingly.To apply a wavelength-modulation technique to the comb-referenced DFG source, the offset-lock frequency of the signal wave is modulated at modulation frequency, fmod = 3 kHz. The signal wave is also modulated, and the DFG frequency is eventually modulated at the same frequency according to Eq. (4).
3. Hyperfine Structure of CH3I
Sub-Doppler resolution spectroscopy of the v 1 band of CH3I was performed using a He-Ne laser [16], a DFG source [6], and an OPO [12], and electric quadrupole hyperfine components induced by the iodine nucleus with the nuclear spin angular momentum I = 5/2 were resolved. The spectral lines recorded using the present spectrometer are as narrow as 280 kHz (HWHM). Therefore, analysis of the measured transition frequencies requires more precise energy expression than in the previous studies [6, 12, 16]. The rotational level structure of the ground vibrational state of CH3I has been extensively studied in microwave spectroscopy, and the rotational and centrifugal distortion constants and the hyperfine coupling constants were precisely determined [17]. The diagonal matrix element of the rovibrational and electric-quadrupole-interaction Hamiltonian is given for the eigenstate as
Here, v is the vibrational quantum number, J is the rotational angular momentum quantum number, K is the projection along the molecular axis, and F is the quantum number for the total angular momentum , where J is the rotational angular momentum. The first term of Eq. (5) is the rovibrational energy, and the second term is the electric-quadrupole-interaction energy given asThe vibration-dependent electric quadrupole coupling constant is (eqQ)v; the vibrtion- and rotation-dependent constants are χ v,J , χ v,K , and χ v,D; and Y(I, J, F) is the Casimir function. No off-diagonal elements of the Hamiltonian are considered.4. Experiment Apparatus
Figure 1 depicts the experiment setup of the spectrometer. The DFG source, CEAC, and OFC are similar to those of the previous works [6, 7]. Briefly, a DFG source consists of a 1.55-μm extended-cavity laser diode (ECLD) and a fiber amplifier as a signal source, a 1.064-μm Nd:YAG laser as a pump source, and a waveguide-type periodically poled lithium niobate (PPLN). The CEAC has two identical concave mirrors with 99.0% power reflectivity at 3.4 μm. They are separated by 23.6 cm, which corresponds to a free spectral range of 636 MHz and a finesse of 303; they also work as optical windows. The power level of the pump source is about 100 mW, and that of the signal source is about 50 mW: the wavelength conversion efficiency of the PPLN is 10%/W. The generated idler wave is thereby evaluated as 500 μW. The electric field strength is estimated as 5 V/m at the antinodes in the CEAC, assuming that the coupling efficiency with the CEAC is 50% and that the electric field strength is enhanced 15 times that of the incident wave. The tuning range is 3 THz limited by the PPLN. The idler wave transmitted through the CEAC is received by a liquid-nitrogen-cooled InSb detector. The OFC is an Er-doped mode-locked fiber laser with an average power of a few milliwatts. The repetition frequency frep of about 67 MHz is phase-locked to a frequency synthesizer referenced to a rubidium atomic clock linked to the TAI through the Global Positioning System (GPS), and the standard deviation of the repetition frequency is less than 0.5 mHz for a gate time of 1 s. Part of the OFC output, whose spectrum is broadened using a fiber amplifier and a highly nonlinear fiber, is used to provide the beat note with the pump wave.
Fig. 1 Experiment setup. A 3.4-μm idler wave is generated in the PPLN. The pump source is a Nd:YAG laser and the signal source is an ECLD. The frequencies of the pump and signal waves are phase-locked to an OFC, and the idler wave frequency is swept by changing the frep. All synthesizers are linked to the Temps Atomique International (TAI). OBPFs are optical band-pass filters, BP is a Brewster plate, CS is a current source, and TMP is a temperature controller.
Figure 2 presents a schematic of the frequency control, which is modified from the previous work [7]. The pump and signal frequencies are phase-locked to the nearest individual comb modes with an offset-lock frequency of 21.4 MHz. In contrast, in the previous work [7] the signal frequency was stabilized at the resonant frequency of the CEAC, which was further stabilized to the Lamb dip of the particular transition. The signal-to-noise ratio of the beat note between the pump (signal) wave and the OFC mode is better than 30 dB at a 300-kHz resolution bandwidth. The bandwidth of the servo control is approximately 50 kHz for the pump source and 150 kHz for the signal source. This servo control reduces the linewidth of both the signal wave and the idler wave. The resultant linewidth of the idler wave is evaluated as narrower than 50 kHz (HWHM) by observing the beat note between the idler wave and the 3.39-μm He-Ne laser wave. The tight phase-locking of the pump and signal sources to the single OFC cancels the effects of the carrier-envelope-offset frequency of the OFC in the idler wave and reduces the linewidth of the idler wave. In contrast, the linewidth of the idler wave in the previous work [7] was not as narrow as that in the present work because the signal wave was tightly locked to the longitudinal mode of the CEAC but the longitudinal mode was loosely locked to the Lamb dip with the slow servo control. The CEAC mode in the present scheme is stabilized to the idler frequency using the Pound-Drever-Hall (PDH) method, in which the signal wave is phase-modulated by an electro-optic modulator (EOM) at 10.7 MHz, and the idler frequency is accordingly modulated at the same frequency. The idler wave reflected from the CEAC is detected by another InSb detector. The detected signal is demodulated by a double-balanced mixer to generate an error signal, which is fed back to two PZTs of the CEAC. The idler frequency is swept by varying the repetition frequency of the OFC by sweeping the output frequency of the frequency synthesizer. The sweep step is 0.01 Hz corresponding to 13.2 kHz for the idler wave, and the sweep rate is 10 (20) ms/step for CH4 (CH3I) limited by the response time of the repetition frequency control. The repetition frequency varies a maximum of 70 Hz, corresponding to 90 MHz in idler frequency which is limited by the capture range of the servo control of the Nd:YAG laser.
The power drift of the idler wave causes variation of the spectral baseline and washes out the spectral lines in the simple absorption spectrum recorded during long accumulation over the repetitive frequency sweep. Wavelength modulation is applied to avoid the degradation. The offset-lock frequency between the ECLD and the nearest comb mode is modulated by 3 kHz. Accordingly, the idler frequency is modulated, and the longitudinal mode frequency of the CEAC follows the modulation. The transmission signal is detected and demodulated at 3 kHz (1f detection) using a lock-in amplifier, and the output is converted to digital data using a 16-bit data acquisition board. The recorded spectra are averaged in a PC, while the idler frequency is repeatedly swept back and forth.
To determine the idler frequency using the OFC, it is necessary to determine the difference in mode number in Eq. (4). The existing data of the ν1 band of CH3I [18] were provided by FTIR spectroscopy with a typical uncertainty in frequency determination of 60 MHz. Because the repetition frequency of the OFC is 67 MHz, the transition frequency must be determined with an uncertainty of less than 20 MHz. To this purpose, we determine the coarse transition frequency of CH3I using the CH4 line as a reference [7] in Doppler-limited resolution spectroscopy. Figure 2 illustrates the experiment setup. The idler wave from the PPLN is divided into two beams, which enter two absorption cells filled with CH4 and CH3I respectively. Each transmitted wave is detected by an individual InSb detector, and the detected signals are simultaneously recorded using a digital oscilloscope. The idler frequency is swept by varying the signal frequency through applying a triangular voltage to one of the PZTs of the ECLD, while the pump wave is frequency-locked to the nearest OFC mode, and the repetition frequency of the OFC is fixed. Parts of the ECLD and OFC outputs overlap at a beam splitter and are detected by an InGaAs photodiode. The detected signal, which contains the optical beat note, is led to a 10.7 MHz band-pass filter (BPF). When the signal frequency crosses one comb mode frequency, the beat signal passes through the BPF twice when the difference between the signal and comb frequencies coincides with ± 10.7 MHz. Consequently, the beat signals appear on the oscilloscope at an interval of 21.4 MHz per comb tooth crossing. This method of generating frequency markers has already been demonstrated in the measurement of the microcavity dispersion [19]. Figure 3 depicts the observed spectra of CH4 and CH3I and frequency markers generated from the beat note. The OFC mode numbers near the CH4 lines are yielded using the previous measurement [7], and the corresponding mode numbers for the CH3I lines are determined by counting the number of the markers between the CH4 and CH3I lines.
Fig. 3 Observed Doppler-limited absorption spectra of CH3I (black) and CH4 (red). The blue curve is the frequency marker, which is magnified in (b).
5. Results
Figure 4 plots the wavelength-modulation spectrum of the v 3 band P(7) F2(2) line of 12CH4. It is averaged over 10 back-and-forth frequency sweeps and it takes 1 min. The horizontal scale indicates absolute frequency. The spectrum is recorded six times, and each is fit to the first derivative of a Lorentz profile function. Adjustable parameters in the fit are transition frequency, line intensity, line width, and slope and intercept of the background. The averaged transition frequency of the six measurements is 88 376 181 604.2 (23) kHz, where the number in parentheses is uncertainty in the unit of the last digit (i.e. 88 376 181 604.2 ± 2.3 kHz). This uncertainty is determined by the standard deviations of the six measurements, whereas each standard deviation in the individual fit is less than 1 kHz. The averaged transition frequency agrees with the CIPM recommended value of 88 376 181 600.5 (20) kHz within the uncertainties. This transition was also used as a reference in the previous work [7], in which the signal and pump frequency was stabilized to the Lamb dip and the averaged transition frequency was 88 376 181 600.3 (21) kHz. Even though the discrepancy from the CIPM value was only –0.2 kHz, the standard deviation due to the repeatability was similar to that in the present work where the idler frequency is phase-locked to the OFC. The recorded spectral line is 230 kHz (HWHM) wide, and the contributions of the transit-time and pressure broadenings are estimated to be 72 kHz and 24 kHz at 0.4 Pa [20]. The remaining line width is attributed to power broadening, even though no quantitative measurements are carried out for the various incident power levels.
Fig. 4 Recorded spectrum of the P(7) F2(2) line of 12CH4. The black dots denote the recorded spectrum, and the red curve denotes the calculated spectrum. The horizontal axis is absolute frequency.
Figures 5 and 6 depict wavelength-modulation spectra of the v 1 band P(J = 22, K = 6), and P(23, 5) transitions of 12CH3I. Each spectrum is typically averaged over 40 back-and-forth sweeps, which require 30 min. By reducing the sample pressure to 0.4 Pa and the incident DFG power level to 500 μW where the PDH method manages to work, the recorded line width typically decreases 280 kHz (HWHM), which is one third less than that of the previous work [12]; thus, six intense hyperfine components (ΔF = ΔJ = –1) are completely or partly resolved. The background is slightly tilted because of Doppler broadening. Each recorded spectrum is fit to a superposition of six first-derivatives of a Lorentz profile function. The adjustable parameters of the fit are six transition frequencies, six line intensities, six line widths, and the slope and the intercept of the background. Table 1 lists the transition frequencies averaged over three measurements along with the uncertainty
Here σ is the standard deviation of three measured frequencies. The value of 3.7 kHz is the systematic shift of the present spectrometer, which is estimated from the discrepancy between the 12CH4 P(7) F2(2) line frequency measured above and the CIPM recommended value. The typical uncertainty is 5 kHz, which is one order of magnitude smaller than that of the previous work [12]. We did not consider any systematic shifts which could contribute to the final uncertainty budget.Fig. 5 Recorded spectrum of P(22, 6) transition in the v 1 band of 12CH3I. The red curve denotes the calculated spectrum.
Fig. 6 Recorded spectrum of P(23, 5) transition in the v 1 band of 12CH3I. The red curve denotes the calculated spectrum.
Table 1. Measured transition frequencies. F” is the total angular moment of the lower level. Obs. – Cal. is the observed transition frequency minus the transition frequency calculated from the determined constants in Table 2.
The measured frequencies in Table 1 are fit to Eq. (5) and Eq. (6) to derive the hyperfine coupling constant of the v1 = 1 state and the rovibrational energy difference between the lower and upper levels, . Table 2 lists the determined molecular constants. Here, the hyperfine coupling constant of the ground state and the rotation-dependent constants of the ground and v1 = 1 states are fixed at the values of the ground state given by Carrocci et al. [17], who analyzed the available literature data of rf and microwave spectroscopy. The determined hyperfine coupling constants agree with each other within the uncertainty. They are also consistent with the values reported in [6] and [16]. The residuals between the observed and calculated frequencies are presented in Table 1.
Table 2. Determined molecular constants
6. Discussion and conclusion
The present spectrometer enables us to measure the transition frequency of weak spectral lines with a relative uncertainty at the 10−11 level. The DFG source, OFC based on TAI, the CEAC, and the frequency control systems must be adequately tuned. In addition, wavelength modulation is applied to overcome the power drift of the idler wave and to enhance sensitivity. This allows us to reduce the sample pressure and the DFG power in order to reduce the line width of the Lamb dips. However, it also distorts the spectral line shape, which leads to a systematic shift of the determined transition frequency on the order of 10 kHz. To reduce the systematic shift, the electronic signals are carefully isolated from each other, and a precision voltage reference IC is employed to cancel the offset voltage of the error signal. Consequently, the sensitivity of the spectrometer is enhanced more than one order of magnitude compared with 12CH4 of the previous paper [7], while uncertainty in frequency determination remains at a similar level.
We have developed a frequency-comb-referenced DFG spectrometer for sensitive and precise spectroscopy. Sub-Doppler-resolution spectra of CH4 and CH3I are recorded using wavelength modulation and data accumulation over repetitive frequency sweeps. The measured transition frequency of CH4 agrees with the CIPM recommended value with a discrepancy of 3.7 kHz. The spectral lines of CH3I are typically 280 kHz wide (HWHM) limited by power broadening. The transition frequencies of the hyperfine-resolved lines are determined with a typical uncertainty of 5 kHz. The hyperfine coupling constant and the uncertainties in the v1 = 1 state of CH3I are consistent with those of the previous work [6]. This frequency-comb-referenced spectrometer enables us to determine the precise frequency of weak transitions recorded in a sub-Doppler resolution spectrum. Indeed, it has already been applied to forbidden transitions in the v 3 band of 12CH4 and has contributed to improving the rotational constant of the ground vibrational state [15].
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