We have demonstrated microwave optical double resonance spectroscopy of the ν1 + ν3 and ν1 + 2ν4 bands of ammonia in a hollow-core photonic bandgap fiber. Signal strength and lineshapes are analyzed. Spectroscopic assignments of previously assigned lines and previously proposed assignments have been confirmed and new assignments have been made. Several microwave transitions in the excited vibrational states have been measured for the first time.
©2010 Optical Society of America
Microwave optical double resonance (MODR) is a widely used nonlinear spectroscopy technique for quantum number labeling of complex infrared and optical spectra. The technique relies on knowledge of measured microwave frequencies assigned to rotational transitions in the ground vibrational state and allows microwave transition in excited vibrational and electronic states to be measured. The MODR technique is useful even for smaller molecules like ammonia, where the overtone and combination bands are very congested. There are many examples of the application of the MODR technique in connection with infrared fundamental molecular bands and with molecular electronic bands . In the latter case it is usually the change in fluorescence from the excited electronic state that is monitored. However, there are very few examples of MODR spectroscopy associated with infrared overtone and combination bands [2–5]. This is mainly due to the fact that these infrared transitions are much weaker than the fundamental bands. Nonlinear spectroscopy techniques associated with overtone and combination bands have often required enhancement cavities [2,3], molecular beam techniques  or pulsed techniques  to achieve adequate signals.
Gas-filled Hollow-core Photonic Bandgap Fibers (HC-PBFs) allow the confinement of light at high intensity over long interaction paths. This confinement makes nonlinear optical interaction possible at low optical power. Acetylene has been studied in detail due to its relatively high absorption strength [6–10] and potential application as optical frequency standard . Atoms are more difficult to load into the fiber, but nonlinear interaction with rubidium has been demonstrated at extremely low optical power . Weaker molecular transitions can be studied by proper adjustment of optical power, gas pressure and fiber length. We have demonstrated sub-Doppler spectroscopy on the relatively weak ν1 + ν3 and ν1 + 2ν4 combination bands of ammonia in a 3 m HC-PBF with an excellent signal to noise ratio . Bhagwat and Gaeta have recently reviewed the nonlinear optics experiments with gas-filled HC-PBFs .
The aim of this work is to demonstrate that the MODR technique can be applied in connection with HC-PBFs. Rather than aiming at an extensive spectroscopic investigation, the work focuses on a demonstration of the capabilities of the technique illustrated with a few selected examples. Although quantitative theoretical calculations of MODR signals are beyond the scope of this paper, a qualitative description of the technique is given. Figure 1 shows a typical infrared transition in the ν1 + ν3 band of ammonia. Due to the inversion symmetry of ammonia, each state is split into a doublet; the symmetric (s) and the anti-symmetric (a) states. The laser radiation in Fig. 1 is absorbed near resonance, but the absorption is reduced if the laser power is sufficiently strong to excite an appreciable fraction of the ground state molecules into the excited state.
This optical saturation gives an imbalance between the a and s ground state populations. Therefore, a resonant microwave field transferring molecules from the a ground state to the s ground state will cause a small increase in the absorption of the infrared transition. Similarly, a resonant microwave field transferring molecules from the s excited state to the a excited state will cause a small increase in the infrared absorption due to the removal of molecules from the excited s state. Thus, amplitude modulation of a resonant microwave field induces a weak amplitude modulation of the near-resonant laser field transmitted through the gas. This modulation can be observed by lock-in detection.
2. Experimental setup
Our experimental setup is similar to configurations reported in the literature for MODR spectroscopy [1,15] except for the replacement of the conventional microwave wave-guide gas cell with a gas-filled HC-PBF placed inside a microwave wave-guide. An outline of the setup is shown in Fig. 2 . The output from an external cavity diode laser (ECL, New Focus 6262) is amplified to 70 mW by an erbium doped fiber amplifier (EDFA). The linewidth of the laser is below 1 MHz, and a calibrated wavelength meter (Burleigh WA-1500) is used as the wavelength reference. The amplified laser is coupled into free-space by lens L1. The beam is transmitted through angled anti-reflection coated windows into the vacuum chamber and coupled in and out of the HC-PBF by lenses L2 and L3. A 3 m long HC-PBF from NKT Photonics (type HC19-1550-01 with a 20-μm diameter core) is used. Approximately 70% of the optical power is transmitted through the fiber at wavelengths off-resonance with molecular absorption lines. About 20 cm of each fiber end is placed inside the vacuum chamber; the rest is placed inside the waveguide. Apiezon vacuum sealing is used to seal the 0.3 mm holes in the vacuum chamber through which the fiber is inserted.
A microwave synthesizer and an amplifier generate about 100 mW of RF power in the frequency range 18 – 26.5 GHz, which is transmitted through the microwave waveguide. This frequency range covers most of the ground state inversion transitions of ammonia. The microwave radiation is amplitude modulated at 10 kHz with a measured modulation depth of about 80% at low power. At average power levels above 60 mW the microwave amplifier starts to saturate, and the modulation depth is reduced to about 55% at 120 mW measured average RF power. The HC-PBF enters and exits the waveguide through 1 mm diameter holes in H-bends (not shown) at either end of the 1-m long microwave system. The HC-PBF makes a double pass inside the waveguide totaling an absorption path length of 2 m where the molecules are susceptible to the microwaves. The fiber outside the waveguide is used for making the connection to the vacuum chamber at one end and making a loop outside the waveguide at the other end.
After evacuation, the chamber is filled with ammonia, which then diffuses into the fiber. The diffusion limited equilibrium time for the actual fiber length, core diameter and average molecular speed is about 30 minutes . However, the strong adsorption of ammonia to the vacuum chamber walls and the inner surface of the HC-PBF extend the equilibrium time significantly, thus at least 100 minutes are allowed to elapse after each change in pressure before measurements are performed.
A photodetector (PD, New Focus Model 2033) is used for monitoring the optical beam. The MODR signal is recovered by phase-sensitive detection using a lock-in amplifier (LI, Stanford Research Systems SR850). Depending on the transition, the most favorable situation is either parallel or perpendicular polarization of the optical and RF fields. In the experiment the microwave radiation is vertically polarized, but the polarization of the optical field is not controlled and it is expected to change through the waveguide.
3. MODR signal analysis
In this section the dependence of the MODR signal on optical and microwave power, optical and microwave detuning as well as gas pressure is investigated. The isolated PP(5,3)s line at 1531.5835 nm  is chosen for this investigation. In the following, RF power levels will refer to the average power measured with an RF power meter at one end of the waveguide. Optical power will refer to the off-resonant power measured at the photodetector position after passing through the HC-PBF. We normalize all our MODR spectra by taking the rms-voltage at the 10 kHz modulation frequency as recorded by the lock-in amplifier and divide it with the off-resonant DC voltage from the photodetector. This relative MODR signal is then a dimensionless quantity representing the relative change in optical transmission induced by the microwave field.
For the investigation of the lineshape of the MODR signal the gas pressure (25 Pa), the optical power (50 mW), and the RF power (95 mW) are fixed at their optimum values, which will be identified below. The Doppler-broadened optical transmission profile is shown in Fig. 3 (curve a), as a function of the optical detuning. From this curve a Naperian absorbance of α = ln[I offRes/I res] = 0.09 is determined, where I res is the transmitted optical power at zero detuning and I offRes is the transmitted power off-resonance. The off-resonance frequency dependent structure is due to the frequency dependent transmission of the HC-PBF itself. The corresponding relative MODR signal is shown as curve b, where the microwave detuning is fixed at 0 MHz. It is noted that the maximum relative MODR signal of 100 × 10−6 corresponds to the rms-voltage at the amplitude modulation frequency being 10 000 times smaller than the DC voltage. The relative MODR signal is insensitive to the off resonance frequency dependent HC-PBF transmission. Curve b fits a Gaussian profile perfectly as seen from curve c, representing the residual from the Gaussian fit.
The Gaussian FWHM width from the fit is 613 MHz, whereas the calculated Doppler width is ΔfFWHM = λ−1(8kT ln2/M)½ = 584 MHz. The 5% discrepancy is most likely dominated by the calibration our frequency scale with an expanded (95% coverage probability) relative uncertainty of 5%.
When the optical detuning is fixed at 0 MHz and the microwave frequency is swept across resonance, we obtain the relative MODR signal shown in curve d in Fig. 3. Note that the horizontal scale for this curve has been expanded so that the RF detuning is given in units of 0.1 MHz. This curve fits a Lorentzian profile, with the residual shown in curve e. The small structure seen in curve e is probably caused by an observed frequency dependent coupling of microwave radiation into the waveguide. The Lorentzian FWHM width of 36 MHz agrees well with the (38 ± 4) MHz transit time broadening obtained by extrapolating the ammonia saturation spectroscopy data in Ref , Fig. 7 to zero pressure. Note that the MODR data presented here are obtained with the same fiber as used in Ref . The same saturated absorption data predict a homogeneous broadening of (43 ± 4) MHz at 25 Pa. This is somewhat larger than what we observe in Fig. 3 for the same pressure, but the absorption line in Fig. 3 and the line used in Ref , Fig. 7 may have different collisional broadening coefficients.
The lineshapes in Fig. 3 are measured at relatively low pressure, where the attenuation of the optical field along the fiber can be neglected. For pressures above 150 Pa the resonant optical field is attenuated significantly along the fiber, which reduces the relative MODR signal. Off-resonance, the attenuation is smaller, and therefore the observed relative MODR signal as a function of optical detuning becomes double-peaked with a local minimum at zero detuning as shown in Fig. 3 curve f.
The amplitude of the relative MODR signal depends on the ammonia pressure. This dependence is studied by changing the pressure in the vacuum box. After each pressure change at least 100 minutes are allowed to elapse in order to reach equilibrium. The Naperian absorbance at resonance is measured for each pressure level and shown in Fig. 4 (a) . The observed linear dependence is expected when the pressure broadening is much smaller than the Doppler broadening. The amplitude of the relative MODR signal for 95 mW RF power and 50 mW optical power is shown in Fig. 4 (b). We assume that the depletion of the optical field through the fiber as well as the increased collision rate cause the decrease in signal amplitude above 30 Pa. A similar decrease in signal amplitude is observed together with an increased linewidth at higher pressure levels in saturation spectroscopy of ammonia .
The relative MODR signal amplitude at different power levels is measured at a pressure of 25 Pa and at zero detunings. The result for fixed RF power (95 mW) and varying optical power is shown in Fig. 5 as squares. The fact that this relative signal depends on the optical power shows that it is indeed a nonlinear phenomenon requiring some saturation of the optical transition. At very high optical power it is expected that the signal amplitude will return towards zero since strong saturation reduces the absorption and hence reduces the effect of the microwave field. The available power is not sufficient to reach the maximum in relative MODR signal; however, the deviation from a linear dependence is observed.
With the optical power fixed at 50 mW, the amplitude of the relative MODR signal as a function of RF power is measured at the same pressure level. The result is shown in Fig. 5 as filled circles. A clear maximum is observed, although a monotone dependence on RF power approaching a maximum is expected when the power is sufficient to make the populations in the two ground states equal. The maximum is caused by saturation of the microwave amplifier and hence reduction in modulation depth at the higher power levels. The dependence of modulation depth on RF power has been measured. The obtained data (filled circles in Fig. 5) can be fitted to a model including the measured modulation depths and a second order polynomial in RF power describing the relative MODR signal amplitude for 100% modulation depth. From this model the expected relative MODR signal amplitude is calculated as a function of RF power for a constant modulation depth. This result is shown as open circles in Fig. 5.
4. Spectroscopic assignments
The observed MODR signals chosen for discussion are listed in Table 1 . Several of the infrared transitions are the same as those observed and discussed in our recent work on saturation spectroscopy in ammonia . We estimate the expanded uncertainties (95% coverage probability) of measured wavelengths and microwave frequencies in Table 1 to be 10% of the FWHM linewidths in Fig. 3, which corresponds to 0.5 pm for optical wavelengths and 4 MHz for microwave frequencies. The ground state microwave frequencies are obtained from ref .
The MODR technique is demonstrated for three different types of transitions originating in the (6,3) ground state levels as shown in Fig. 6 . These transitions are the ΔK = −1 PP(6,3)s and PP(6,3)a transitions and the ΔK = + 1 RP(6,3)s and RP(6,3)a transitions, both of the ν1 + ν3 combination band, as well as the ΔK = −1 PP(6,3)s and PP(6,3)a transitions of the ν1 + 2ν4 combination band. MODR signals associated with the ground state inversion transition at 19756 MHz are observed for all six transitions and are listed in Table 1. The PP(6,3)s transition of the ν1 + ν3 band was assigned by  while an assignment of the corresponding PP(6,3)a transition was proposed by . In the latter work it was concluded that the excited states were perturbed. The observed MODR signals associated with the two infrared transitions and the ground state inversion transition at 19756 MHz confirms the assignments. The excited state inversion transition can be calculated from the measured wavelength of the two optical transitions and the frequency of the ground state splitting to be (66.88 ± 0.09) GHz or (2.231 ± 0.003) cm−1 in agreement with the 2.228 cm−1 obtained in . Similar combination relations of the transitions associated with the ν1 + 2ν4 band result in a calculated excited state inversion frequency of (38.70 ± 0.09) GHz or (1.291 ± 0.003) cm−1 in excellent agreement with the −1.290 cm−1 estimated in . The negative sign indicates that the s level is above the a level as shown in Fig. 6. The excited state frequency for the RP(6,3) transitions is within the range of our microwave equipment, and the observed frequency of 15891 MHz is consistent with the value (15.98 ± 0.09) GHz calculated from combination relations.
The PP(7,6)s and PP(7,6)a transitions were assigned in  having the frequencies 6514.069 cm−1 (1535.139 nm) and 6513.651 cm−1 (1535.237 nm), respectively. Ref. . did not include these transitions in the overall fit of the spectrum due to the assumption that the excited state energy levels appeared to be perturbed. In the present work, MODR signals at these optical wavelengths involving the known ground state inversion transition at 22925 MHz associated with (J,K) = (7,6) were not observed. However, MODR signals at this inversion frequency were instead observed at the infrared frequencies of 6510.9902 cm−1 and 6510.0903 cm−1 corresponding to the wavelengths 1535.8647 nm and 1536.0770 nm. These two frequencies are associated with unassigned transitions in ref . Therefore, it is proposed that the PP(7,6)s and PP(7,6)a transitions are associated with the latter two frequencies.
The PP(7,7)s and PP(7,7)a transitions were not reported assigned in  and the term values for the excited state not listed in . However, as mentioned above, the PP(7,6)s transition was assigned to occur at 6514.069 cm−1 (1535.139 nm), but a corresponding MODR signal was not observed. Instead, a MODR signal is observed when the microwave frequency is tuned to 25716 MHz, suggesting that the ground state is (J,K) = (7,7). MODR signals were observed at the laser wavelengths 1535.0979 nm and 1535.1389 nm corresponding to the PP(7,7)s and PP(7,7)a transitions, respectively. A combination of the frequencies of the infrared transitions and the microwave transition results in an excited state inversion transition with a frequency of (20.50 ± 0.09) GHz, which is in excellent agreement with the observed frequency of 20493 MHz. These infrared assignments of the PP(7,7) transitions have to our knowledge not been reported previously.
In our previous work  we showed that the four transitions PP(5,3)s, PP(5,3)a, PP(6,6)s and PP(6,6)a are close lying transitions and the PP(5,3)a, and PP(6,6)a transitions were resolved. The latter two are overlapping under Doppler broadened spectroscopy. The PP(5,3)s transition is discussed in the detailed investigation in the previous sections. The frequencies of the two ground state transitions associated with the four infrared transitions have been reported to be 21285 MHz and 25056 MHz, respectively, for the (5,3) and (6,6) inversion transitions . We have observed the MODR signals for these four optical transitions at the microwave frequencies associated with the inversion transitions (5,3) and (6,6) of the ground states. From combination relations we find the excited state (4,2) inversion transition to have the frequency (8.65 ± 0,09) GHz, which was predicted by  to be 8.66 GHz. This frequency is outside the range of our present set up. The excited state (5,5) inversion transition was observed directly from the MODR signal at 21209 MHz and calculated from combination relations to be 21.20 GHz. These values do not agree with the value of 25.06 GHz from ref . The reason is most likely that the excited state levels are perturbed, which is also suggested in ref . There has been some discussion concerning the correct a and s ordering. In ref . it was suggested that the PP(6,6)s transition corresponds to the transition at 1531.6513 nm while Refs [19,21]. suggest that this is the PP(6,6)a transition, although Ref. . indicate that the assignment is tentative. The observation of the excited state microwave transition at 21209 MHz indicates that the s-inversion component has the larger frequency and thus corroborates our assignment as indicated in Table 1. It is noted that an accurate frequency measurement of the 1531.6513 nm line has been reported by Czajkowski et. al.  resulting in a wavelength of 1531.6515 nm.
The PP(4,2)s and PP(4,2)a transitions cannot be distinguished under Doppler broadened spectroscopy. In our recent work  the two lines were resolved and the microwave inversion transition in the excited state was predicted to occur at 22.22 GHz. The microwave inversion transition in the (4,2) ground state is known to have the frequency of 21703 MHz. For the laser tuned to each of the two infrared transitions, MODR signals were observed at 21703 and 22224 MHz, respectively. The latter inversion splitting was also predicted in recent work by Xu et.al . to occur at 0.739 cm−1 (22.15 GHz).
We have reported, what to the best of our knowledge is the first observation of MODR in a HC-PBF. Double resonance signals are not easily observed by conventional techniques in these relative weak combination bands. We have observed MODR signals associated with the ν1 + ν3 and ν1 + 2ν4 combination bands of ammonia. The observations have confirmed previously assigned infrared transitions and suggested several new assignments (see Table 1). Microwave inversion transitions in the two combination bands have been observed and compared with calculated values indicating that there are a number of perturbations in the excited states. A detailed study of the dependence of the MODR signal on optical and microwave power and on pressure has been made and the conditions for optimal signal to noise ratio reported. MODR lineshapes have been investigated.
The reported work was limited in microwave frequency range; however, the technique can easily be extended to a wider range by using the appropriate microwave waveguides.
References and links
1. H. Jones, “Infrared-Microwave Double Resonance Techniques,” in Modern Aspects of Microwave Spectroscopy, G. W. Chantry, ed., (Academic Press, N.Y., 1979).
2. C. Ishibashi, R. Saneto, and H. Sasada, “Infrared radio-frequency double resonance spectroscopy of molecular vibrational-overtone bands using a Fabry-Perot cavity-absorption cell,” J. Opt. Soc. Am. B 18(7), 1019–1029 (2001). [CrossRef]
3. A. Czajkowski, A. J. Alcock, J. E. Bernard, A. A. Madej, M. Corrigan, and S. Chepurov, “Studies of saturated absorption and measurements of optical frequency for lines in the ν1 + ν3 and ν1 + 2ν4 bands of ammonia at 1.5 microm,” Opt. Express 17(11), 9258–9269 (2009). [CrossRef] [PubMed]
4. U. Merker, H. K. Srivastava, A. Callagari, K. K. Lehmann, and G. Scoles, “Eigenstate resolved infrared and millimeter-wave-infrared double resonance spectroscopy of methylamine in the N-H stretch first overtone region,” Phys. Chem. Chem. Phys. 1(10), 2427–2433 (1999). [CrossRef]
5. S. L. Coy and K. K. Lehmann, “Modeling the rotational and vibrational structure of the i.r. and optical spectrum of NH3,” Spectrochim. Acta 45A, 47–56 (1989).
6. F. Benabid, F. Couny, J. C. Knight, T. A. Birks, and P. St. J. Russell, “Compact, stable and efficient all-fibre gas cells using hollow-core photonic crystal fibres,” Nature 434(7032), 488–491 (2005). [CrossRef] [PubMed]
7. S. Ghosh, J. E. Sharping, D. G. Ouzounov, and A. L. Gaeta, “Resonant optical interactions with molecules confined in photonic band-gap fibers,” Phys. Rev. Lett. 94(9), 093902 (2005). [CrossRef] [PubMed]
8. J. Henningsen, J. Hald, and J. C. Petersen, “Saturated absorption in acetylene and hydrogen cyanide in hollow-core photonic bandgap fibers,” Opt. Express 13(26), 10475–10482 (2005). [CrossRef] [PubMed]
9. R. Thapa, K. Knabe, M. Faheem, A. Naweed, O. L. Weaver, and K. L. Corwin, “Saturated absorption spectroscopy of acetylene gas inside large-core photonic bandgap fiber,” Opt. Express 31, 2489–2491 (2006).
11. K. Knabe, S. Wu, J. Lim, K. A. Tillman, P. S. Light, F. Couny, N. Wheeler, R. Thapa, A. M. Jones, J. W. Nicholson, B. R. Washburn, F. Benabid, and K. L. Corwin, “10 kHz accuracy of an optical frequency reference based on (12)C2H2-filled large-core kagome photonic crystal fibers,” Opt. Express 17(18), 16017–16026 (2009). [CrossRef] [PubMed]
12. P. Londero, V. Venkataraman, A. R. Bhagwat, A. D. Slepkov, and A. L. Gaeta, “Ultralow-power four-wave mixing with Rb in a hollow-core photonic band-gap fiber,” Phys. Rev. Lett. 103(4), 043602 (2009). [CrossRef] [PubMed]
15. J. Henningsen and J. C. Petersen, “Infrared-microwave double resonance in methanol: coherent effects and molecular parameters,” J. Opt. Soc. Am. B 5(9), 1848–1857 (1988). [CrossRef]
17. C. H. Townes, and A. L. Schawlow, Microwave Spectroscopy (McGraw-Hill, N.Y., 1955).
18. L. Lundsberg Nielsen, F. Hegelund, and F. M. Nicolaisen, “Analysis of the high-resolution spectrum of ammonia (14NH3) in the near-infrared region, 6400-6900 cm−1,” J. Mol. Spectrosc. 162(1), 230–245 (1993). [CrossRef]
19. L.-H. Xu, Z. Liu, I. Yakovlev, M. Yu. Tretyakov, and R. M. Lees, “External cavity tunable diode laser NH3 spectra in the 1.5 μm region,” Infrared Phys. Technol. 45(1), 31–45 (2004). [CrossRef]
20. L. Li, R. M. Lees, and L.-H. Xu, “External cavity tunable diode laser spectra of the ν1+2ν4 stretch-band combination bands of 14NH3 and 15NH3,” J. Mol. Spectrosc. 243(2), 219–226 (2007). [CrossRef]
21. R. M. Lees, L. Li, and L.-H. Xu, “New VISTA on ammonia in the 1.5 μm region: Assignments for the ν3+2ν4 bands of 14NH3 and 15NH3 by isotopic shift labeling,” J. Mol. Spectrosc. 251(1-2), 241–251 (2008). [CrossRef]