# Passage And Resonance In Synergy – PARIS: A molecular jet chirp- and tone-excitation Fourier transform microwave spectrometer for broad acquisition and high resolution

Ha Vinh Lam Nguyen, Sven Herbers, Xavier Landsheere, Jens-Uwe Grabow

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Ha Vinh Lam Nguyen, Sven Herbers, Xavier Landsheere, Jens-Uwe Grabow. Passage And Resonance In Synergy – PARIS: A molecular jet chirp- and tone-excitation Fourier transform microwave spectrometer for broad acquisition and high resolution. Review of Scientific Instruments, 2025, 96 (5), 10.1063/5.0256434. [https://arxiv.org/abs/2005.05426]

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# Passage And Resonance In Synergy - PARIS: A molecular jet chirp- and tone-excitation Fourier transform microwave spectrometer for broad acquisition and high resolution

Ha Vinh Lam Nguyen,<sup>a,b*</sup> Sven Herbers,<sup>a</sup> Xavier Landsheere,<sup>a</sup> and Jens-Uwe Grabow<sup>c</sup>

<sup>a</sup> Univ Paris Est Creteil and Université Paris Cité, CNRS, LISA, F-94010 Créteil, France

<sup>b</sup> Institut Universitaire de France (IUF), 1 rue Descartes, F-75231 Paris, France

<sup>c</sup> Institut für Physikalische Chemie und Elektrochemie, Lehrgebiet A, Callinstrasse 3a, D-30167 Hannover, Germany.

* Corresponding author. Email: lam.nguyen@lisa.ipsl.fr

## ABSTRACT

Jet-expansion Fourier transform microwave (FTMW) spectroscopy is a powerful technique for investigating isolated molecules and molecular aggregates. The Coaxial Beam-Resonator Arrangement (COBRA) offers unrivalled resolution, but requires repetitive frequency retuning of a high-Q resonator for survey spectra using short, resonant single-tone excitation pulses. Chirp-excitation methods, using a fast but powerful frequency-ramp signal passing over spectral line positions, dramatically reduce survey time, but at the cost of lower resolution and sensitivity for individual lines. As a consequence, many laboratories employ both spectrometer types. However, setting up individual machines with their own vacuum systems, high-frequency electronics, and control software is costly and time-consuming. We developed and constructed the PARIS (Passage And Resonance In Synergy) FTMW spectrometer, operating in the 2-20 GHz range, integrating both tone-excitation and chirp-excitation techniques in a single, resource-efficient setup: Using a modular design, most electronic components serve dual-purpose, with integration of reflector-refocused and resonator-enhanced interaction setups in a spherical high-vacuum chamber. The chirp and single-tone excitation setups are arranged perpendicularly, with instant mode-switching, both using microwave propagation coaxial with the molecular jet-expansion. PARIS achieves a sensitivity of a few parts-per-billion (ppb) for OCS diluted in Neon (1%) on the resonator axis and a few parts-per-million (ppm) on the broadband axis. A resolution (full width at half maximum, FWHM, of the amplitude spectrum) of ~2 kHz is attained with both experiments, capable of resolving complex hyperfine structures, such as those from two <sup>14</sup>N nuclei of 4-methylpyrimidine already in broadband operation at minimum resolvable peak separation matching the respective FWHM.
<figure><img src="image_3.png" /></figure>

Graphical abstract:

Pulsed Resonator
(COBRA)

(-) narrow instantaneous
bandwidth

(++) highest sensitivity

(++) highest resolution

<figure><img src="image_4.png" /></figure>

Fast Passage
(IMPACT)

(++) wide instantaneous
bandwidth

(+) high sensitivity

(+) high-resolution

(++) spectral details at highest-resolution with highest sensitivity

(++) rapid surveys at highest resolution with high sensitivity
# I. INTRODUCTION

Molecular jet Fourier Transform MicroWave (FTMW) spectroscopy is a powerful tool for studying isolated molecules in the gas phase where a very low rotational temperature near the thermodynamic zero point $T \le 2$ K can be reached [1]. The most attractive advantage of employing a molecular jet-expansion is the adiabatic cooling of the sample to a very low rotational energy comparable to the rotational energy spacing ($k_B T \approx hB$), resulting in a significant simplification of the observed spectra. It increases thereby the signal-to-noise-average-ratio (SNR) due to collisional depopulation of rotationally and vibrationally excited states, leading to large population differences for transitions originating from molecular states $\le k_B T$ [2]. Today, molecular jet FTMW spectrometers in the frequency range below 26 GHz are commonly used and have shown great sensitivity and resolving power. They are suitable for volatile molecules ($\le 30$ atoms), including species important for atmospheric or bio-chemistry, the latter often requiring additional measures, e.g. LASER-ablation or heating, to seed the carrier gas prior to its expansion.

The classical version of supersonic jet FTMW spectrometers is the Balle-Flygare set-up employing a pulsed jet expanding perpendicular to the axis of a Fabry-Pérot-type resonator [3]. The development on resonator machines was largely concluded in the 1990s with the design of the coaxially oriented beam-resonator arrangement (COBRA) [4]. Today's resonator setups are based on this optimized design and have an unrivalled resolution. However, they are constrained by the time required for spectral surveys, as the high-Q resonator requires mechanical tuning at each frequency step, which is typically about 300 kHz ($\sim 10^{-5}$ cm$^{-1}$). An approach to overcome this problem is the use of fast frequency ramps irradiating the sample rather than employing Fourier-limited short single-tone pulses building-up an electromagnetic field inside a resonator. First demonstrated by Flygare, employing an analog voltage-controlled swept source to achieve a chirp excitation, its digital implementation was developed a decade ago using a digital/analog-converter (DAC) based arbitrary waveform generator (AWG), which delivers fast frequency-ramp signals at band widths of >1 GHz ($> 3333 \times 10^{-5}$ cm$^{-1}$), thereby being able to reduce the time requirements for surveys dramatically [5]. Developments on the chirp excitation technique are on-going, e.g. a coaxial jet-ray design achieving high-resolution broadband spectra in 2012 [6], coupling a chirp spectrometer to a vacuum-ultra-violet photoionization mass spectrometer in 2018 [7], millimeter-wave chirp spectrometers [8,9], and $K_a$-band chirp spectrometers [10,11]. These new implementations of the chirp excitation
PLEASE CITE THIS ARTICLE AS DOI: 10.1063/5.0256434

technique, and variations within them, show a still increasing efforts in exploiting the large
frequency coverage obtainable via chirp-excitation.

Although the common high-Q resonator-based spectrometers can provide better
resolution on specific spectral features of a target molecule, chirp-excitation FTMW provides
better time-efficiency for highly complex broadband spectra of species carrying strong signals
(i.e. visible in a spectrum obtained from a single experiment in the high-Q resonator) arising,
e.g., from mixtures of reaction products, isomers, or non-covalently bound molecular
aggregates. In many studies where optimizations of the supersonic expansion is required in the
absence of reliable spectral predictions, like large van der Waals complexes or spectral studies
on electric discharges to produce ions or radicals, employing a chirp-excitation machine is
indispensable [12-15]. It is necessary to monitor a wide spectral range in real-time in order to
recognize changes in the spectrum while the experimental conditions are varied. Furthermore,
the line intensities of chirp-excitation spectra, as long as obtained at conditions sufficiently
below effective π/2 conditions, are more reliable than those of a resonator-based apparatus. This
is an important feature for assignments of the spectra and for conformational analysis.

Despite all advantages of a chirp-excitation spectrometer, the higher resolution and
sensitivity of the resonator-based setups cannot be replaced. Today, many laboratories engaged
in microwave spectroscopy rely on both, a chirp- and a tone-excitation molecular jet FTMW
spectrometer [16-33], even though the doubled equipment at state-of-the-art level for the
electronics and the vacuum system, to the most part being the same for both techniques, is cost-
intensive.

We developed and implemented a FTMW spectrometer capable of both techniques with
an innovative and resource-efficient approach: Using a modular design, most electronic
components will be used in a dual-purpose with integration of reflector-refocused and
resonator-enhanced interaction setups in a spherical high-vacuum jet-expansion chamber. The
chirp- (Fig. 1b) and tone- excitation (Fig. 1a) spectrometers are perpendicularly arranged in a
single spherical high-vacuum jet-expansion chamber, forming the “Passage And Resonance In
Synergy” (PARIS) instrument, allowing for use of chirp- or tone-excitation with instant turn-
over (Fig. 1c). This highly integrated experimental setup - built at much lower costs than two
individual spectrometers - offers the advantages of both techniques: Rapid broadband
capabilities, intensity reliability, as well as unrivalled resolving power and sensitivity.
This is the author's peer reviewed, accepted manuscript. However, the online version of record will be different from this version once it has been copyedited and typeset.
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<figure><img src="image_5.png" /><figcaption>FIG. 1. The PARIS spectrometer (c) integrates two setups, fast Passage (b) And short Resonance (a) In Synergy.</figcaption></figure>

## II. CONCEPT OF THE PARIS SPECTROMETER

### A. Electronic design

A block diagram of the supersonic-jet PARIS-FTMW spectrometer is presented in Fig.

2. PARIS utilizes the In-phase/quadrature-phase (I/Q) Modulation Passage-Acquired Coherence Technique (IMPACT) implemented by ramped single sideband frequency conversion. The spectrometer then uses chirp or single-tone MW signals for fast passage or pulsed resonance excitation, respectively, employing components that allow for frequency coverage from 6 to 20 GHz or 2 to 20 GHz, respectively.
This is the author's peer reviewed, accepted manuscript. However, the online version of record will be different from this version once it has been copyedited and typeset.
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<caption>FIG. 2. The standard set-up of the supersonic-jet PARIS-FTMW spectrometer.</caption>

(1) I/Q Arbitrary waveform generator, Keysight M9336A, 16 bit, 540 MHz; (2a/b) Fast pulse/timing preamplifier, Fast ComTech TA2400, DC-875 MHz, 2Vpp; (3) Analog signal generator, National Instruments PXIe-5654; (4a-e) PIN-diode SPDT RF-switch, Kratos-General Microwave F9025; (5) Single sideband I/Q-modulator, Miteq SM0226LC1MDQ; (6) Programmable attenuator, 26.5 GHz, 11 dB, 1 dB steps, Keysight 84904K; (7) Programmable step attenuator, 26.5 GHz, 90 dB, 10 dB steps, Keysight 84906K; (8) Attenuator switch driver, Keysight 11713B; (9a/b) Directional coupler 16 dB, Krytar 102020016; (10a/b) Power sensors, Keysight E4413A; (11) Power meter, dual channel, Keysight N1914A; (12a-d) Electro-mechanical SPDT RF-switches, 26.5 GHz, Keysight 8765C; (13) Pulse power amplifier, AA Matech AAMCS-AMP-6G-18G-43dB-43dBm-0-C, 6-18 GHz, 43 dBm; (14a-h) Flexible coaxial cable, DC-26 GHz, Thorlabs KMM4/8/36; (15a-j) Hermetic-seal coaxial-feedthrough, Huber&Suhner 455-34SMA5003111NE; (16) Quad-ridge horn antenna, MVG Satimo QH2000, 2-32 GHz; (17a/b) Offset parabolic reflector, MVG Satimo SR40A, 6-32 GHz; (18) Roof-top reflector, aluminum; (19a/b) Solenoid valve, General Valve Series 9; (20) Valve controller, dual channel, General Valve Iota one; (21) MW power limiter 0.01-26.5 GHz, Keysight N9356C; (22) Low noise amplifier, 2-20 GHz, Narda-Miteq LNA-30-02002000-27-10P; (23) Power amplifier, Keysight 83020A, 2-26 GHz, 23dBm; (24a-d) Flexible coaxial cable, DC-26GHz, Thorlabs KMM4/8/36; (25a-c) Termination 50 Ω; (26) Planar reflector, aluminum, d = 630 mm, Eilhauer; (27) Spherical reflector R = 1260 mm, d = 630 mm, Eilhauer; (28a/b) Linear translation stage, IGUS SHT-12-C2AT1-A0C0B-AF1F1AA; (29) Stepper motor drive, National Instruments MID-7604; (30) Motion control I/O, National Instruments PXI-7344; (31a/b) Low noise amplifier, 2-20 GHz, Narda-Miteq LNA-30-02002000-27-10P; (32) Crystal detector, Keysight 8473C; (33) Low noise amplifier, Narda-Miteq AMF-7D-0100200-22-

<figure><img src="image_6.png" /></figure>
10P; (34) Image rejection I/Q-demodulator, Narda-Miteq IRM0226LC1Q; (35a/b) Low pass filter, Mini-Circuits ZX75LP-470-S+; (36) Digital Oscilloscope, National Instruments PXIe-5162, 2 channels, 10 bit, 1.5 GHz; (37) System computer, National Instruments PXIe-8880 Controller, Keyboard, Monitor; (38) Multi-I/O Data acquisition, National Instruments PXIe-6341; (39) Timing-I/O data acquisition, National Instruments PXIe-6612; (40) System chassis, National Instruments PXIe-1085; (41) Experiment sequencing logic, Leibniz Universität Hannover PXI-timing/control; (42) Rb frequency standard, Stanford research system FS725; (43a-h) DC-power supply, +/- 5V, +/- 12 V, +/- 15 V, +/- 24 V, Keysight U8001A; (44a/b) Pressure sensor, HV, Pfeiffer CMR361; (45) Pressure sensor, UHV, Pfeiffer CMR365; (46) Pressure meter, Six channel, Pfeiffer TPG 366; (47) Spherical vacuum chamber, six-way cross DN630 ISO-K, Neyco; (48) Diffusion pump, DN630 ISO-F, 20000 L/s, Leybold DIP20000; (49) Roots pump, 251 m³/h, Leybold RUVAC WS 251; (50) Rotary vane pump, 65 m³/h, Leybold TRIVAC D65B.

## PARIS primary signal generation

The major of components employed in the PARIS spectrometer's operational modes are identical. A primary signal with frequency v is generated by the signal generator (3), which is either used for excitation (red signal path) or for detection (blue signal path) by employing a PIN-diode single-pole-double-throw (SPDT) switch (4d).

## PARIS in the fast-passage chirp excitation mode

For the excitation, a short MW frequency ramp (chirp) centered at v will be created with sufficient MW power for the fast passage excitation of the molecules. For the detection, the molecular MW response has to be down-converted, taken as a difference frequency signal between the molecular and the primary radiation at frequency v, into a lower-frequency band (base band). For the molecular excitation, the primary signal source is not directly utilized, but the output signal of a single sideband up-converter (5). A broadband (up to 1 GHz) single-sideband frequency ramp v + Δv(t) is created via I/Q modulation at frequencies Δv(t) in the range -500 to +500 MHz, centered at DC, invoking an arbitrary signal generator employing two channels (1). As a consequence of two RF signals swept from 500 MHz through DC and back to 500 MHz while alternating the quadrature phase sense, two frequency half-bands (the lower and the upper sides) are generated, thus creating the broad-band frequency ramp centered at v. This ramp, with its generation principle warranting invariant phase repeatability by design, i.e., without needing a phase-locked-loop (PLL), is used for excitation after having been amplified by two fast pulse/timing preamplifiers (2a/b), one for each output channel of (1). The
power level necessary for the polarization of the molecular systems is adjusted either via the
amplitude of the modulation frequency or, preferably, using two variable attenuators (6,7)
controlled by an attenuator switch driver (8) which is also programmed to establish a safe
maximum input level for the high-power solid-state amplifier (13). High power levels become
necessary because of the spectral width of 1 GHz, which is swept fast, typically in τp ≤ 10 µs.
To monitor the input level, a directional coupler (9a) provides a fraction of the power (–16dB)
to a power sensor (10a) connected to a two-channel power meter (11). Since employing a pulse
amplifier (13), no PIN-diode SPDT switch at its output is needed for noise suppression during
the detection phase. The electro-mechanical SPDT switch (12a) will route the excitation signal
from the pulse amplifier either to the dual-polarization quad-ridge horn-antenna (16) or to the
L-shaped antenna located at the planar reflector (26). If the switches (12a/b) are set for the
chirp-excitation mode (purple signal path), the energy of the excitation signal emerges as
linearly polarized curved wavefront from the horn antenna (16), passes the off-axis parabolic
reflector (17a) achieving a planar wavefront, to be refocused on the region of the jet-expansion
in front of the roof-top reflector (18) after passing the opposing off-axis parabolic reflector
(17b) thus providing an enhanced MW field amplitude for molecular polarization. The jet
originates from the solenoid valve (19a) controlled by the valve driver (20). The excitation field
interacts twice with each volume element of the molecular jet, that is before and after passing
the roof-top reflector, resulting in polarizations that contribute to molecular responses
propagating parallel or anti-parallel with the jet-expansion, respectively, i.e. red- and blue-
shifted signals. With either the excitation field or the molecular response to it passing the roof-
top reflector, both, the red- and the blue-shifted molecular signals' polarization directions are
rotated by 90° with respect to the linearly polarized wave emerging from the quad-ridge horn
(see Fig. 3). The molecular response, containing signals within the range v – 500 to v + 500
MHz is then received at the perpendicular polarization direction by the horn antenna (16) and
passes the power limiter (21) which protects the delicate MW receiver electronics from the
harmful power levels of the frequency ramp excitation.

The molecular signal is raised in amplitude by a very-low-noise amplifier (22) followed
by a second low-noise amplifier (33) after routed back to the common signal path by the electro-
mechanical SPDT switch (12b). The combined gain is chosen to be just sufficiently high for
the insertion losses in the subsequent stages of the signal processing only having a negligible
impact on the SNR, thus realizing the widest possible dynamic range at optimum sensitivity.
Two PIN-diode SPDT switches (4e/c) between these two amplifiers protect the subsequent
electronics from saturation by the chirp power still passing the limiter (21) and ensuring
matched impedance at the first amplifier's output and second amplifier's input during the excitation, respectively. To quantify the power level of the fast passage excitation signal leaking through the front-end receiving stage of the spectrometer, a directional coupler (9b) between the pin-diode switch (4e) and the crystal detector (32) provides a fraction of the power (–16dB) to a power sensor (10b) connected to a two-channel power meter (11).

<figure><img src="image_7.png" /><figcaption>FIG. 3. In the quasi-coaxial jet and rooftop & parabola arrangement of PARIS, the axis of the molecular jet and the axis of the wave propagation are co-linear in the horn-parabola-parabola-plane. The dual-path excitation at 0°/90°-polarization excitation fields before/after rooftop-reflection results in red/blue-shifted 90°/90°-polarization emission fields at dual-polarization horn.</figcaption></figure>

By selecting the appropriate primary frequency v, any desired 1 GHz band region of the spectrum limited by the frequency range of the signal generator (3) and the high-power amplifier (13) can be set. Thus, a spectral range of up to 1 GHz bandwidth can be obtained with a single measurement, enabling rapid survey measurements, acquired in a segmented scans within the spectrometer's operational boundaries of 6-20 GHz.

### PARIS in short-resonance tone excitation mode

For the molecular excitation, the output signal of the single sideband up-converter (5) is now employed to generate a short, resonant single-tone pulse used to build-up a strong electromagnetic field at very narrow-band width (≈ 0.3 MHz = 0.00001 cm⁻¹) governed by the
This is the author's peer reviewed, accepted manuscript. However, the online version of record will be different from this version once it has been copyedited and typeset.

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pulse duration and the spectral width of a high-Q resonator employed for enhancement. A single-sideband signal at frequency $v + \Delta v$ is created via I/Q modulation with a single frequency $\Delta v$ in the interval -500 to +500 MHz, invoking the arbitrary waveform generator (1), which provides two channels. The two RF I/Q-signals at $\Delta v$ create a single-tone at an offset of $\Delta v$ from $v$. In the tone-excitation mode, the power requirements are less than for the chirp-excitation mode. While the amplifier (13) might produce up to 20 W for the chirp-excitation mode, a power of only a fraction of a mW up to a few 100 mW, depending on the polarity of the molecule, is sufficient here. The power level necessary for the polarization of the molecular systems is adjusted by the two variable attenuators (6,7) controlled by an attenuator switch driver (8) which is also programmed to establish a maximum input level to avoid saturation of the high-power solid-state amplifier (23). The electro-mechanical SPDT switch (12a) will route the signal either to the dual-polarization quad-ridge horn-antenna (16) or to the L-shaped antennae located at the flat reflector (26). If the switches (12a/b) are set for the short-resonance single-tone excitation mode (green signal path), the energy of the excitation signal builds-up a standing-wave field inside the semi-confocal resonator formed together with the opposing spherical reflector (27) thus providing an enhanced MW field amplitude for molecular polarization. The electro-mechanical SPDT switch (12c) selects one of two antennae pointing in perpendicular directions away from the reflector's center, i.e. two orthogonal polarization directions. The short excitation impulses are formed by the envelop of the I/Q-modulation signal and the PIN-diode SPDT-switches (4a/b) which are also isolating the two antennae from the idle-noise of the amplifier (23) during the detection of the molecular pulse response. Both reflectors can be adjusted by the linear-translation stages (28a/b) with its stepper-motor drive (29) supervised by a motion controller (30) to obtain a resonance condition, but we mostly only adjust the spherical reflector. The excitation signal polarizes the molecular ensemble in the jet-expansion originating from the solenoid valve (19b) controlled by the valve driver (20). The molecular response, linearly polarized in the direction of the transmitting antenna, is received by one of the two receiving antennae oriented in the same direction, impedance-matched to the resonator while the PIN-diode switches (4a/b), at high-impedance, are isolating the first pair of antennae. Both pairs of antennae are located on reflector (26), with the antennae belonging to the same polarization placed diametrically to its center at equal distance pointing away from it. After passing the molecular response to the respective very-low-noise amplifiers (31a/b), the signals are fed into the electro-mechanical SPDT switch (12d). Two PIN-diode SPDT switches (4e/c) protect amplifier (33) and the subsequent electronics from saturation by the single-tone power impulse, ensuring matched impedance at the input of amplifier (33) and the output of
amplifiers (31a/b) during the excitation, respectively. The first PIN-diode switch (4e) also allows, via the crystal detector (32), for monitoring of a signal wobbled across the mode pattern of the Fabry-Pérot-type resonator, being generated by I/Q-modulation during the tuning process to obtain a resonance condition.

To perform a broadband spectral survey limited by the frequency range of the signal generator (3) and the high-power amplifier (23), a stepped scan with the resonator tuned automatically in-between measurements can be acquired within the spectrometer's operational boundaries of 2-20 GHz.

## PARIS molecular signal detection

Via the single sideband (de)modulator (34), the broadband molecular response is converted back to the base band centered at DC, with $\Delta v = -500$ to +500 MHz as I/Q signal pair, i.e. negative and positive frequency signals that differ in quadrature phase sense. The frequency conversion from and back to the base band, in a single conversion step each, minimizes jitter, i.e. destructive phase fluctuations. The low-pass filters (35a/b) reject signals beyond the Nyquist frequency limit according to the folding theorem of the discrete Fourier transform. The A/D-conversion is accomplished by the transient recorder (36) which provides two-channel quadrature detection. The spectral composition of the transient emission is obtained after performing a Fourier transform in the data acquisition, control, and analysis system (37, 38, 39) hosted in a 19" PXIexpress chassis with the experiment sequence logic (41) clocked by a Rubidium time standard (42), ensuring timing- and phase-stability. The DC power supply (43) provides DC voltages needed for the PIN-diode SPDT switches and some other components with small power requirements.

Because the extremely weak molecular signal is often far below the thermal noise level, phase-synchronized repetitions are crucial to improve the SNR by the phase-correct addition of individual measurements. The signal provided by the Rb frequency standard (34) is used for generating all analog frequency signals and for deriving all digital clock rates. Only if all signal sources used in the system are referenced to the same 10 MHz frequency standard, it becomes possible to generate the molecular signal with recurring phase. The 10 MHz signal is distributed through several independent channels, as required by the spectrometer's components.
## B. Mechanical design

### Off-axis parabolic reflector – Semi-confocal resonator arrangement

Both, the high-resolution single-tone excitation and the broadband chirp excitation arrangements of PARIS, use a microwave propagation coaxial with the molecular jet-expansion while being arranged perpendicularly to each other in the spherical chamber of PARIS (see Fig. 1c). The tone-excitation's Fabry-Pérot-type resonator has a semi-confocal configuration, consisting of a planar and a spherical reflector. The chirp-excitation's free-space arrangement uses two parabolic reflectors with off-axis feeds, one hosting a dual-polarization quad-ridge horn-antenna, with the two orthogonal directions employed as transmitting and receiving channels, and one hosting a roof-top reflector. Details will be given in the following sections.

Contrasting a molecular jet-expansion being injected perpendicular to the symmetry axis of the Fabry-Pérot-type resonator, the resolution as well as the sensitivity of the acquired spectra could be significantly increased with the introduction of the Coaxially Oriented Beam Resonator Arrangement (COBRA). Realizing a quasi-coaxial arrangement with the two off-axis parabolic reflector facing each other, both advantages are also achieved in the I/Q-Modulation Passage-Acquired Coherence Technique (IMPACT). Combining both approaches, the PARIS arrangement depicted in Fig. 1c shows the jets' sources at the center of the resonator's planar reflector and at the center of the roof-top reflector.

### Vacuum chamber

The vacuum chamber of PARIS is a DN630 ISO-K stainless-steel six-way cross with spherical center body, illustrated in Fig. 4. One of the six DN630 ISO-K ports attaches directly to a DN630 ISO-F oil diffusion pump (8), all other five ports are closed by DN630 ISO-K - DN320 ISO-F reducing flanges (4). Three DN320 ISO-F ports are closed with DN320 ISO-K plexi-glass flanges. The two other DN320-F ports host DN320 ISO-K - DN250 ISO-K adaptor flanges (5) featuring six DN40 ISO-KF ports on its circumference. The DN40 ISO-KF ports host DN40 ISO-KF flanges equipped with vacuum feedthroughs for electronic and microwave cables. Both DN250 ISO-K ports, separated by two pneumatic gate valves (6), are attached to DN250 ISO-K stainless steel six-way crosses (7). Using the six-way crosses as transfer chambers to the planar and the roof-top reflector's back sides, the two setups enable manipulations at each valve's nozzle and sample supply without breaking the main chamber's vacuum. Four of the remaining five DN250 ISO-K ports of each six-way cross are closed with stainless steel or plexi-glass flanges, as desired. The port opposite to the gate valve is closed with a stainless steel
<figure><img src="image_8.png" /></figure>

flange hosting a rotating feedthrough (Pfeiffer DN40-ISOKF) for a 12 mm outer-diameter stainless steel tube mounting the pulse valve and electronic feedthroughs for operating the valve and sample supply, including heating, DC-discharge, and LASER-ablation. The use of a solenoid valve (Parker, General Valve series 9) not only reduces the gas load for the pumping system, thereby decreasing the capacity requirements, it also combines ideally with the fast-passage and short-resonance excitation schemes of PARIS. The diluted gas mixture, typically ~1% in a noble gas at a total pressure in the range of 0.5 to 5 bar, is expanded into the evacuated chamber (3). The nozzle, in its simplest design, consists of a round orifice of 0.5 – 2.0 mm diameter, with an exit channel 2 mm in length, which expands conically to 4 mm. The properties of the exiting gas pulse are of both qualitative and quantitative significance for the rotational spectrum of the molecular system detected by these methods, i.e., the effective translational, rotational, and vibrational temperature of the species, as well as their spatial distribution and the chemical nature of the systems present in the jet.

<figure><img src="image_9.png" /><figcaption>FIG. 4. The vacuum chamber of PARIS (dimensions in mm) at the Fabry-Pérot-type resonator side-view. (1) Aluminium reflectors, $σ = 1.6 \times 10^7$ 1/Ωm conductance, distance d = 530 to 730 mm, radius a = 315 mm, curvature r = 1260 mm for the spherical reflector; (2) Linear translation stage, IGUS SHT-12-C2AT1-A0C0B-AF1F1AA, 100 mm hub, 0.5 µm resolution, 25 mm/s velocity; (3) Stainless steel six-way cross DN630 ISO-K, 1130 mm inner diameter, spherical center body; (4) Reducing flange DN630 ISO-K to DN320 ISO-F; (5) Adapter flange DN320 ISO-K to DN250 ISO-K with six DN40 ISO-KF ports; (6) Gate valve DN250 ISO-F, VAT; (7) Stainless steel six-way cross DN250 ISO-K; (8)</figcaption></figure>
This is the author's peer reviewed, accepted manuscript. However, the online version of record will be different from this version once it has been copyedited and typeset.
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Oil diffusion pump DN630 ISO-F, Leybold DIP20000, 20000 L/s pump capacity; (9) 3-stage
mechanical pump system, Leybold RUVAC WS251/TRIVAC D65B, 210/65 m³/h capacity.

Mounting frame

A mounting system is required for the two reflectors (26, 27) forming the semi-confocal Fabry-Pérot-type resonator placed between two linear translation-stage pairs, as well as the two parabolic reflectors, facing each other to form a free-space arrangement while fed off-axis by the quad-ridge horn antenna and the roof-top reflector. The mounting frame consists of 12 stainless steel bars of quadratic (10 x 10 mm) cross-section and 630 mm length (shown in black in Fig. 5) connected by 12 W-shaped stainless-steel angles (blue), to form a 670 x 670 mm cube held in place by eight 20 x 20 mm plastic cubes (green) at its corners, each having a set-screw. Two pairs of two L-shaped angles (pink) are used to attach each reflector to the linear translation stage. The larger L-shaped angle, holding the mirror from its back side, is made from plastic to insulate the reflector electrically, all other mounting parts are stainless steel. An aluminum ring of 154 mm outer diameter, 130.5 mm inner diameter, and 6.5 mm thickness is used to affix the L-shaped angles to the back of the reflectors. The smaller L-shaped angles are used to connect the plastic angles to the linear-translation stages, with the stages affixed to the mounting frame by stainless steel C-shaped pieces (red). The increase stability, the two upper as well as the two lower stages are connected via pairs of L-shapes angles attached to aluminum rings of 308 mm outer diameter, 261 mm inner diameter, and 8 mm thickness.

<figure><img src="image_10.png" /><figcaption>FIG. 5. The mounting frame in the vacuum chamber of PARIS looking (a) perpendicular to the resonator axis, showing the two reflectors of the semi-confocal Fabry-Pérot-type resonator supported by the two pairs of linear-translation stages, and (b) perpendicular to the free-space electromagnetic wave propagation axis, showing the two parabolic reflectors, the off-axis quad-ridge horn antenna, and the off-axis roof-top reflector. Figure (c) displays the chamber's interior looking parallel to the parabola off-axis feeding directions, i.e. perpendicular to the resonator's axis.</figcaption></figure>
To host the free-space arrangement formed by the parabolic reflectors facing each other, two pairs of parallel stainless-steel bars, as illustrated in Fig. 5, are used to clamp the two reflectors together at their feeding arms. The complete system, with horizontal feeding directions from the horn and the roof-top reflector, is then bolted to the mounting frame.

## Reflector design

a) The *PARIS Fabry-Pérot-type resonator* uses a semi-confocal construction with a planar reflector and a spherical reflector with a radius of curvature $r = 1260$ mm, as illustrated in Fig. 6. Both reflectors exhibit five bores of 20 mm diameter at 2 mm thickness remaining to the reflector's surface with an orifice of 5,66 mm to it. The center bore is for the pulse valve, the four surrounding bores are for two pairs of antennae, arranged horizontally and vertically. The valve and antennae are mounted in the planar reflector, with the bores in the spherical reflector closed by stainless steel cylinders. The two antennae pairs are orthogonal at different symmetric distances to the center bore. Typically, the longer antennae, at a larger distance of 50.05 mm from the center, are adjusted for the frequency ranges 2-8 GHz, while the shorter antennae, at smaller distance of 33.68 mm from the center, are adjusted for the frequency range 8-20 GHz. Other ranges can be achieved by tailoring the antennae's length and their gap to the reflector's surface. The antennae are made from the inner conductor of a semi-rigid microwave cable such that they fit into a female-female SMA feed-through mounted via an insert to the 20 mm bores. The L-shaped antennae's geometries were optimized empirically by minimizing the measured VSWR (Voltage Standing Wave Ratio) to match the impedance of the high-Q resonator, i.e., to achieve critical coupling.
<figure><img src="image_11.png" /><figcaption>FIG. 6. Design of the planar reflector (upper part) and the spherical reflector (lower part). The reflector's entire view is seen to the left while the enlarged center of the reflector is seen to the right. φ and ϑ indicate the two cross-sections rotated by 90° to illustrate the positions of the five bores. At the planar reflector, the bore pair with larger distance hosts the longer antennae and the bore pair with smaller distance hosts the shorter antennae. The bore in the middle accepts the solenoid valve. In the current setup, all bores of the spherical reflector are closed by stainless steel cylinders. All values are given in mm.</figcaption></figure>

b) *The PARIS off-axis parabola & rooftop reflectors* arrange the axis of the molecular jet and the axis of the wave propagation co-linear in the parabola-rooftop-axis (see Fig. 5). Therefore, each rotational transition also appears as a Doppler doublet. The dual-path excitation at 0°/90°-polarization excitation fields before/after rooftop-reflection results in red/blue-shifted 90°/90°-polarization emission fields at dual-polarization quad-ridge horn (see Fig. 5). The design of the rooftop reflector is illustrated in Fig. 7. The bore in the back accepts the solenoid valve.
<figure><img src="image_12.png" /><figcaption>FIG. 7. Rooftop reflector viewed from the side (left), from the top (middle), and from its back (right). All values are given in mm.</figcaption></figure>

### C. PARIS instrument control, data acquisition, and spectral analysis program

Complementing the PARIS hardware, the FTMW++ software [6] has been developed further to enable seamless interplay between fast-passage IMPACT and short-resonance COBRA operation. Instantaneous, automated switching between chirp- and tone-excitation modes enables broadband survey spectra at high-resolution with auto-location of line-patterns followed by the acquisition of ultimate resolution spectra at no turn-around time. An example of the software's graphical user interface (GUI) is shown in Fig. S-I of the supplementary material as well as on the monitor screen of Fig. 8a.

### III. PERFORMANCE OF PARIS

The PARIS spectrometer, shown in Fig. 8, is the first implementation of an FTMW spectrometer that offers at the same time the ultimate resolution and sensitivity of the short, resonant single-tone microwave excitation pulse COBRA technique with the rapid survey capability at the same resolution of a microwave chirp-excitation IMPACT instrument.
<figure><img src="image_13.png" /><figcaption>FIG. 8. The PARIS-FTMW spectrometer. (a) View on the 19” electronics-rack and the monitor displaying the GUI of the FTMW++ software. (b) View perpendicular to the chirp-excitation IMPACT axis. (c) View perpendicular to the tone-excitation COBRA axis.</figcaption></figure>

A. Detection Threshold

To characterize the detection limits of the PARIS spectrometer, gas mixtures of OCS in Neon (1%) were prepared. OCS is an ideal test molecule, owing to the transition dipole moments and partition function from a significantly polar linear molecule while exhibiting a rather large natural abundance distribution of its isotopologues. The observation of a certain isotopologue can then directly be related to the sensitivity limit in dipole-moment times parts-per-billion of molecules in the gas mixture.

The ¹⁸O¹³C³⁴S isotopologue has a natural abundance of 0.0001%. In the 1% gas mixture with Neon, it is present at 0.000001% corresponding to 10⁻⁸ or 10 parts-per-billion (ppb). Recording a 100 µs time domain signal for 20 000 acquisitions at 10 Hz repetition rate at 1 bar backing pressure using the short-resonance single-tone excitation mode allows for a clear observation of the signal as shown in Fig. 9. Thus, the typical detection limit for molecules with strong rotational lines (small partition functions and large dipole transition moments at integration times less than an hour) is estimated to be in the range of a few ppb for the resonator-
enhanced branch. Using the short, resonant single-tone excitation pulse mode, we measured an extensive series of OCS isotopologues down to the detection limit. A list of all measured transitions is given in the supplementary material.

<figure><img src="image_14.png" /><figcaption>FIG. 9. The $J'←J'' = 1←0$ transition of the $^{18}O^{13}C^{34}S$ isotopologue at natural abundance (0.0001%) in a 1% mixture with Ne recorded with the PARIS short-resonance setup after 20 000 repetitions at 10Hz repetition rate in the single-tone microwave excitation pulse mode.</figcaption></figure>

In the fast-passage chirp-excitation mode, the sensitivity is lower, suffering from the absence of the emission field enhancing resonator, as only the excitation field's disadvantage can be compensated for by very high-power amplifiers. However, compared to the very limited spectral width of a high-Q resonator, many isotopologues can be observed at once, as shown in Fig. 10; some of them are highlighted in the recorded 1 GHz spectral segment. Using fast-passage chirp-excitation, the isotopologue observable at lowest abundance after 20 000 acquisitions with an SNR of 4 is $^{16}O^{13}C^{34}S$. This isotopologue has a natural abundance of 0.05%. In a 1% gas mixture with Neon, it is then present at 0.0005% or $5 \cdot 10^{-6}$ or 5 parts-per-million (ppm). Therefore, we estimate the detection limit for molecules with strong rotational transitions (small partition functions and large dipole moments at integration times less than one hour) of our broadband experiment to be a few ppm for the free-space branch.
<figure><img src="image_15.png" /></figure>

FIG. 10. A 1 GHz spectral segment of 1% OCS diluted in Neon recorded in the PARIS in the fast-passage chirp excitation mode after 20 000 repetitions at 10 Hz. Besides the $J'←J'' = 1←0$ rotational transition of the main isotopologue $^{16}$O$^{12}$C$^{32}$S, also the transitions of several minor isotopologues are detected in natural abundance; three of them being highlighted. The SNR of the free-space setup is about 2-3 orders of magnitude lower compared to the high-Q resonator-enhanced setup, consistently scaling with the square-root of the resonator's Q.

A further demonstration of the sensitivity of the PARIS spectrometer is its capability to measure many synthesized deuterated thiophene variants and isotopologues. Synthesis results indicate that the singly deuterated thiophene constitutes approximately 9% of the total sample, distributed equally between 2-D and 3-D thiophene (~4.5% each, see Fig. 11a). A gas mixture containing 1% of the synthesized sample in Helium was analyzed. Here, Helium is chosen as our career gas since it provides less efficient cooling compared to Neon or Argon and transitions origination from higher *J* and *K* values remain populated. Using the short-resonance tone-excitation mode, we successfully detected several $^{13}$C isotopologues of 2-D and 3-D thiophene, corresponding to a concentration of ~5 ppm, with very good SNR as illustrated in Fig. 11d. The nuclear quadrupole hyperfine structures (nq-hfs) from the deuterium's spin ($I = 1$) coupling to the overall rotation of the molecule are well-resolved. Although many repetitions were co-added for optimal results, the satisfactory SNR ratio was achieved already after a few hundred repetitions. Notably, this detected isotopologue of deuterated thiophene has a relatively small *a*-dipole moment component of 0.55 D, and the intensity is distributed over all hyperfine components of deuterium. For the 3-D isotopologue, *b*-type transitions were also observed,
This is the author's peer reviewed, accepted manuscript. However, the online version of record will be different from this version once it has been copyedited and typeset.

PLEASE CITE THIS ARTICLE AS DOI: 10.1063/5.0256434

despite the *b*-dipole moment component being only 0.047 D. This observation highlights the sensitivity of the spectrometer, even for transitions induced only by asymmetric deuteration of thiophene.

<figure><img src="image_16.png" /><figcaption>FIG. 11. Deuterated thiophene measurements with the PARIS resonator-enhanced branch. (a) Synthesis scheme with concentration distribution for different deuteration grades determined by NMR analysis. The given percentages are the total values for all deuterated variants. (b) The *a*-type $J'_{K'_a,K'_c} \leftarrow J''_{K'_a,K''_c} = 2_{12} \leftarrow 1_{11}$ transition of the singly deuterated thiophene 3-D with an estimated abundance of ~4.5% and an estimated *a*-dipole moment of 0.55 D, obtained after 66 repetitions. (c) The *b*-type $J'_{K'_a,K'_c} \leftarrow J''_{K''_a,K''_c} = 1_{11} \leftarrow 0_{00}$ transition of the singly deuterated thiophene 3-D with an estimated *b*-dipole moment of 0.047 D, obtained after 3 000 repetitions. (d) The $J'_{K'_a,K'_c} \leftarrow J''_{K''_a,K''_c} = 2_{12} \leftarrow 1_{11}$ transition of the ¹³C-isotopologue of the singly deuterated thiophene 2-D in natural abundance. The spectrum shown was recorded at 20 000 repetitions, nevertheless a satisfactory SNR was achieved already after a few hundred repetitions. (e) The $J'_{K'_a,K'_c} \leftarrow J''_{K''_a,K''_c} = 2_{12} \leftarrow 1_{11}$ transition of the fully deuterated thiophene-d₄ recorded at 3 000 repetitions. The line patterns are from the nq-hfs of the four deuterium nuclei with *I* = 1.</figcaption></figure>

A similar demonstration of PARIS sensitivity is the detection of the *s*-gauche conformer of isoprene. Isoprene exists in two configurations: the *s*-trans conformer (98.5% abundance at
room temperature) and the *s-gauche* conformer (only 1.5%), as illustrated in Fig. 12. Due to its small dipole moment of only 0.25 D, measuring *s-trans* isoprene is very challenging [34,35]. Detecting the *s-gauche* conformer is even more difficult due to its low abundance in combination with an also low dipole moment of 0.36 D. Therefore, it eluded detection until 2019, when a DC-discharge had to be applied to enhance its population [36]. The PARIS spectrometer is sensitive enough to detect *s-gauche* isoprene under standard conditions, without employing a DC-discharge.

<figure><img src="image_17.png" /><figcaption>FIG. 12. (a) The $J'_{K'_a, K'_c} \leftarrow J''_{K''_a, K''_c} = 2_{12} \leftarrow 1_{01}$ transition of *s-trans* isoprene (98.5% abundance at room-temperature) measured with the PARIS spectrometer. (b) The $J'_{K'_a, K'_c} \leftarrow J''_{K''_a, K''_c} = 2_{12} \leftarrow 1_{01}$ transition of *s-gauche* isoprene (1.5% abundance) measured with the PARIS spectrometer under the same conditions. (c) For comparison, the same *s-gauche* isoprene transition previously detected employing DC-discharge to enhance the population [36].</figcaption></figure>

## B. Resolution capability

The smallest separation of two signals that can be resolved into signals with different peak frequencies is on the order of the full line-width at half maximum (FWHM) of isolated lines. The line-width, as observed however, depends on experimental conditions and setup. With the PARIS spectrometer, we can achieve an FWHM of about 2 kHz under ideal conditions. To demonstrate this line-width, we carried out experiments on OCS with a particular focus on the $O^{13}CS$ isotopologue, which shows a spin-rotational splitting of the $J' \leftarrow J'' = 1 \leftarrow 0$ transition of less than 5 kHz.
Experimental conditions

To achieve ultimate resolution, we utilized the low jet-velocity of a mixture of OCS (1%) in Xenon. After the excitation, the molecular response was recorded over a duration of 2 ms. Measurements were carried out for the isotopologues OCS (59 000 averages), OC<sup>34</sup>S (100 000 averages), as well as O<sup>13</sup>CS (469 000 averages). As the signal decays exponentially in the time domain, it is crucial to determine the time window during which the signal still carries information that can be employed to increase resolution. Therefore, the FID was Fourier transformed in 200 µs segments. The SNR of the recorded segments after excitation is shown in Fig. 13a. The final data point with an SNR of approximately 2 occurs at 1485 µs. Beyond this point, at 1485 µs + 200 µs = 1685 µs, the FID no longer contains any information on the transition. However, it does not mean that all signal in the FID before 1485 µs is necessarily useful for maximizing resolution, since Doppler shifts might vary across the recorded segments (according to the angular distribution of the velocity groups). By plotting the Doppler splitting as a function of the FID time segments (see Fig. 13b), a significant velocity spread becomes apparent in the probed molecular ensemble.

<figure><img src="image_18.png" /><figcaption>FIG. 13. (a) Signal to noise ratio for the J'←J'' = 1←0 transition after excitation of 1% OCS seeded in Xenon. (b) The Doppler splitting varying for the time segments. The FID was Fourier transformed in 200 µs segments with the starting time of each segment taken for the time axis.</figcaption></figure>

The Doppler splitting remains relatively constant up to ~1000 µs, with only a slight decrease from 14 kHz to 12 kHz, indicating minimal changes in the velocity distribution of the probed ensemble over time. However, beyond 1000 µs, a sharp decline is observed. A Doppler splitting of 14 kHz at 12163 MHz corresponds to a velocity of 345 m/s. This implies that after
1 ms, the molecule would have traveled ~34.5 cm. Since the microwave excitation begins ~750 µs after opening the pulsed valve to allow for stationary conditions following adiabatic cooling, this corresponds to a total travel path of ~60.4 cm at 1.75 ms travel time, consistent with the dimensions of the resonator (630 – 730 mm). Distribution invariant FIDs are limited to 1100 µs at best and therefore, only the leading 1100 µs should be used.

## PARIS tone-excitation COBRA resolution

In time-domain coherence spectroscopy, when using window functions, the intensity of a signal can be correlated with the achievable resolution, up to the limit that is set by the dimensions of the spectrometer with respect to the velocity of the expanding jet, i.e. its effective transit time. The stronger the signal, the longer the time before the signal of the recorded FID vanishes in the noise floor, and the smaller the ultimately achievable linewidth after windowing.

Fig. 14 shows the FID of OCS in Xenon, where ultimate resolution in terms of FWHM = 2.3 kHz was achieved after application of a Kaiser window (Kaiser parameter $\beta$ = 8.0) [37]. The FWHM was determined by taking the difference between the two frequencies where half of the maximum value in the spectrum is observed.

<figure><img src="image_19.png" /><figcaption>FIG. 14. Achieved resolution in the spectrum of the J'←J'' = 1←0 transition of the parent species of OCS measured in Xenon as career gas, after application of a Kaiser window function, improving the resolution from 3.4 kHz to 2.3 kHz. Upper trace: Original FID and amplitude spectrum after Fourier</figcaption></figure>
transformation. Lower trace: FID with applied Kaiser window applied and corresponding amplitude spectrum.

For OC$^{34}$S and O$^{13}$CS, similar resolution (2.0 kHz and 2.2 kHz, respectively) was achieved, as seen in Fig. 15.

<figure><img src="image_20.png" /><figcaption>FIG. 15. Resolution of the $J'←J'' = 1←0$ transition in the spectra of the OC$^{34}$S and O$^{13}$CS isotopologues measured with Xenon as career gas utilizing the Kaiser window function to improve the resolution. The narrow splitting in the right hand side spectra arises from the spin-rotation coupling of the $^{13}$C nucleus to the overall rotation.</figcaption></figure>

Fine tuning the Kaiser parameter shows that the best resolution for O$^{13}$CS is achieved at $\beta = 8 - 10$, though the difference is not large. The final signal we used to determine the most precise O$^{13}$CS transitions frequencies to date is shown in Fig. 16 (an enlarged version of the lower right part of Fig. 15). There are several benefits of the pulsed jet expansion in an open resonator or dual-path arrangement compared to a continuous molecular beams in conventional experiments: (i) Absolute frequencies, without a-priori knowledge of the jet velocity in a single experiment, can be given, since both symmetrically shifted Doppler components are recorded. (ii) The sample throughput is reduced due to the gas duty-cycle. (iii) The sensitivity for low-$J$ rotational transitions is increased due to the population transfer along collisional (adiabatic) cooling.
<figure><img src="image_21.png" /></figure>

<figure><img src="image_22.png" /><figcaption>FIG. 16. Transition $J'←J'' = 1←0$ of $O^{13}CS$ measured for an 1.3% OCS sample seeded in Xe at 0.5 bar backing pressure with 460,000 repetitions, showing the nq-hfs arising from the $^{13}C$ nucleus. The record length is 1600 µs, with the velocity distribution invariant FID being limited to the leading 1000 µs (see section *Experimental conditions*). Slightly different from Fig. 15, a Kaiser parameter $\beta = 10.0$ was applied in an effort to fine tune the possible resolution. The center frequency and respective FWHM are given at each signal peak. The Doppler splitting is given in blue. The separation of the two hyperfine components of the $^{13}C$ nucleus is 4.7 kHz. The average FWHM is 2.3 kHz. The resolution limit is approximately the FWHM.</figcaption></figure>

A further demonstration of the resolution of the PARIS spectrometer is its capability to resolve the complex fine-hypefine patterns of 3,4-lutidine. The spectrum in Fig. 17 shows its $J'_{K'_a,K'_c} \leftarrow J''_{K''_a,K''_c} = 7_{07} \leftarrow 6_{06}$ transition. The transition includes large amplitude motion (LAM) fine structure comprising five torsional components (00), (01), (10), (11), and (12). They arise from the internal rotation of the two inequivalent methyl groups with intermediate barriers of about 427 cm$^{-1}$ and 512 cm$^{-1}$ [38,39]. Each torsional component appears as triplet due to the nq-hfs caused by the $^{14}N$ nucleus, which overlaps with the torsional fine structure. Each hyperfine component again appears as Doppler doublet. Here, the instrumental 2 kHz resolution limit cannot be achieved due to unresolved splittings from spin-spin and spin-rotation coupling and lower interrogation time due to the use of Neon as carrier gas (jet velocity of about 808 m/s). However, the two lines separated by 3.4 kHz are still partially resolved, and the two lines separated by 4.6 kHz are fully resolved, demonstrating a resolution of about 4 kHz for this molecule.
<figure><img src="image_23.png" /></figure>

FIG. 17. A short-resonance tone-excitation spectrum of the $J'_{K_a,K'_c} \leftarrow J''_{K_a,K''_c} = 7_{07} \leftarrow 6_{06}$ transition of 3,4-lutidine measured in Neon with overlapping fine and hyperfine structures arising from the internal rotation of two inequivalent methyl groups and the spin of the $^{14}$N nucleus. The Doppler splitting is ±53 kHz. Lines separated by 3.4 kHz are still partially resolved while lines separated by 4.6 kHz are fully resolved.

### PARIS chirp-excitation IMPACT resolution

Employing the fast-passage chirp-excitation mode, 1 GHz-segmented survey spectra can be acquired. Due to a quasi-coaxial arrangement of the dual parabola focused wave propagation with the molecular jet emerging from the roof-top reflector, high resolution measurements are well feasible, unlike common chirp-excitation implementations utilizing an expansion perpendicular to the axis between two horn-antennae facing each other. Such a perpendicular arrangement attains resolutions of typically 60 kHz, one order of magnitude less than the resolution attainable with PARIS. Fig. 18 illustrates the spectrum of the $J' \leftarrow J'' = 1 \leftarrow 0$ transition of OC$^{34}$S in Xenon recorded in the short-resonance tone-excitation mode after 20 repetitions and the spectrum of the same transition recorded in the fast passage chirp-excitation mode with a rooftop and parabola arrangement after 20 000 repetitions.
<figure><img src="image_24.png" /></figure>

FIG. 18. Resolutions obtained for the $J'←.J'' = 1←0$ transition of the OC$^{34}$S isotopologue measured with Xenon as career gas. The blue spectrum was recorded in the short-resonance tone-excitation mode taking 20 repetitions and the red spectrum was recorded in the fast-passage chirp-excitation mode with a rooftop and parabola arrangement taking 20 000 repetitions. The FWHM is the same in both measurements, demonstrating that the same resolution is achieved for the tone- and chirp-excitation modes. Coherent molecular emission originating from the excitation field propagating between the parabolic reflectors in both directions, leads to baseline-contributions in between the two Doppler components. With the propagation of the jet and these fields being perpendicular to each other, the day time of this emission is shorter than of the Doppler components. Due to the molecular number density away from the roof-top reflector being small and lower electric field amplitude of the unfocussed field between the parabolic reflectors, these contributions are weak and, depending on the relative phase, tend to appear dispersive when inferring with the inner shoulders of the Doppler doublet.

A similar demonstration of the PARIS chirp-excitation resolution are the measurements of 4-methylpyrimidine, a molecule with dense, narrow nq-hfs signal patterns arising from the nuclear quadrupole coupling of two inequivalent nitrogen nuclei. In addition, the methyl group in 4-methylpyrimidine undergoes internal rotation LAM, making all rotational transitions split into an A and an E torsional symmetry species [40,41]. The left-hand side of Fig. 19 shows a spectrum of the $J'_{K_a,K_c} ← J''_{K_a,K_c} = 4_{04} ← 3_{03}$ E species transition recorded in the short-resonance tone-excitation mode with Neon as carrier gas, with completely resolved nq-hfs of two $^{14}$N nuclei. The right-hand side of Fig. 19 illustrates a small portion of the 1 GHz segment of a fast-passage chirp-excitation spectrum of 4-methylpyrimidine. Even in this broadband mode, the nq-hfs is completely resolved.
<figure><img src="image_25.png" /><figcaption>FIG. 19. Left-hand side: A spectrum of the $J'_{K_a,K_c} \leftarrow J''_{K_a,K_c} = 4_{04} \leftarrow 3_{03}$ E species transition of 4-methylpyrimidine recorded in the short-resonance tone-excitation mode with 1 000 repetitions using Neon as carrier gas, with completely resolved nq-hfs of the two $^{14}$N nuclei. Right-hand side: A small portion of the 1 GHz segment of a fast-passage chirp-excitation spectrum of the same transition recorded with 500 000 repetitions. Also in this mode, the nq-hfs could be completely resolved. Fourier transforms of the unaltered FIDs are illustrated here. Corresponding spectra obtained after application of the Kaiser window (Kaiser parameter $\beta = 4.0$) are in the supplementary materials.</figcaption></figure>

IV. CONCLUSION

To conclude, we return to a statement from the introduction: “Today, many engaged in microwave spectroscopy rely on both, a chirp- and a tone-excitation supersonic jet FTMW spectrometer”, i.e., employing chirp excitation for rapid survey scans, while tone-excitation is reserved for achieving high resolution and ultimate sensitivity where required. Now, with the implementation of PARIS, the chirp-excitation mode achieves the same high resolution as the tone-excitation mode. Still, the tone-excitation mode exhibits a sensitivity that is two to three orders of magnitude higher (ppb compared to ppm). Therefore, investigations routinely begin by taking chirp-excitation spectra, turning out to be fully sufficient in many cases. Only if necessary, the tone-excitation needs to be employed to measure weaker lines that may not be observable in the fast-passage mode, particularly those of minor isotopologues, but importantly, the fast-resonance tone-excitation mode is not required to achieve higher resolution. The PARIS spectrometer combines complete chirp- and tone-excitation machines in a single vacuum chamber and being run from a highly integrated electronic setup. Featuring a coaxial microwave
propagation aligned with the molecular jet expansion for both modes, it shares nearly all electronic components used in either mode without any turn-around time.

With the targeted rotational transitions being electric dipole transitions, PARIS operates on two schemes achieving Rotational Electric Resonance (RER) signals: (i) Utilizing the Coaxial Beam-Resonator Arrangement for high resolution (~ 3 kHz FWHM) at ultimate sensitivity (ppb Deep intensity range, RER D) as well as (ii) utilizing the I/Q Modulation Passage Acquired Coherence Technique for high resolution (~ 3 kHz FWHM) for rapid surveys (> 1GHz broad spectral bandwidth, RER B).

## SUPPLEMENTARY MATERIAL

See the supplementary materials for the list of all measured transitions of several isotopologues of OCS down to the detection limit using the short-resonance single-tone microwave excitation pulse as well as for the two spectra in Fig. 19 illustrated the FTMW++ software's GUI.

## DATA AVAILABILITY STATEMENT

The data that supports the findings of this study are available within the article and its supplementary material.

## ACKNOWLEDGMENTS

This work was supported by the Agence Nationale de la Recherche ANR (project ID ANR-18-CE29-0011) and by the European Union (ERC, 101040480-LACRIDO). The authors extend their gratitude to Thorsten Marioneck and the workshop of the Institutes for Inorganic and Physical Chemistry at RWTH Aachen University for their assistance in producing several mechanical components. We are also grateful to Madeleine G. Adwood and Brian J. Esselman from the University of Wisconsin-Madison for providing the deuterated thiophene sample used in our measurements.
REFERENCES

¹ J-U. Grabow, Fourier transform microwave spectroscopy measurement and instrumentation. In: M. Quack, F. Merkt, editors, Handbook of high-resolution spectroscopy, Chapter 1, Vol. 2, Chichester, Wiley, U.K. (2011).

² J.-U. Grabow, E.S. Palmer, M.C. McCarthy, P. Thaddeus, *Rev. Sci. Instrum.* **76**, 093106 (2005).

³ T. J. Balle, W. H. Flygare, *Rev. Sci. Instrum.* **52**, 33–45 (1981).

⁴ J.-U. Grabow, W. Stahl, H. Dreizler, *Rev. Sci. Instrum.* **67**, 4072 (1996).

⁵ J.J. Pajski, M.D. Logan, K.O. Douglass, G.G. Brown, R.D. Suenram, B.C. Dian, B.H. Pate, *Int. J. high speed electron.* **18**, 31 (2008).

⁶ M. K. Jahn, D. A. Dewald, D. Wachsmuth, J.-U. Grabow, S. C. Mehrotra, *J. Mol. Spectrosc.* **280**, 54–60 (2012).

⁷ S. M. Fritz, B. M. Hays, A. O. Hernandez-Castillo, C. Abeysekera, T. S. Zwier, *Rev. Sci. Instrum.* **89**, 093101 (2018).

⁸ B. M. Hays, T. Guillaume, T. S. Hearne, I. R. Cooke, D. Gupta, O. Abdelkader Khedaoui, S. D. Le Picard, I. R. Sims, *J. Quant. Spectrosc. Radiat. Transfer* **250**, 107001 (2020).

⁹ M. Hermanns, N. Wehres, B. Heyne, C. E. Honingh, U. U. Graf, S. Schlemmer, *Rev. Sci. Instrum.* **94**, 034705 (2023).

¹⁰ T. S. Hearne, O. Abdelkader Khedaoui, B. M. Hays, T. Guillaume, I. R. Sims, *J. Chem. Phys.* **153**, 084201 (2020).

¹¹ K. N. Crabtree, J. H. Westerfield, C. A. Dim, K. S. Meyer, S. L. Johansen, Z. S. Buchanan, P. A. Stucky, *Phys. Chem. Chem. Phys.* **26**, 13694–13709 (2024).

¹² C. Pérez, M. T. Muckle, D. P. Zaleski, N. A. Seifert, B. Temelso, G. C. Shields, Z. Kisiel, B. H. Pate, *Science* **336**, 897 (2012).

¹³ S. I. Murugachandran, J. Tang, I. Peña, D. Loru, M. E. Sanz, *J. Phys. Chem. Lett.* **12**, 1081 (2021).

¹⁴ C. Abeysekera, A. O. Hernandez-Castillo, J. F. Stanton, T. S. Zwier, *J. Phys. Chem. A* **122**, 6879 (2018).

¹⁵ G. B. Park, R. W. Field, *J. Chem. Phys.* **144**, 200901 (2016).

¹⁶ K. N. Crabtree, M. A. Martin-Drumel, G. G. Brown, S. A. Gaster, T. M. Hall, M. C. McCarthy, *J. Chem. Phys.* **144**, 124201 (2016).

¹⁷ S. Mata, I. Peña, C. Cabezas, J. C. López, J. L. Alonso, *J. Mol. Spectrosc.* **280**, 91–96 (2012).
¹⁸ J. L. Alonso, C. Pérez, M. E. Sanz, J. C. López, S. Blanco, *Phys. Chem. Chem. Phys.* **11**, 617 (2009).

¹⁹ E. J. Cocinero, A. Lesarri, P. Écija, J.-U. Grabow, J. A. Fernández, F. Castaño, *Phys. Chem. Chem. Phys.* **12**, 12486–12493 (2010).

²⁰ I. Uriarte, P. Écija, L. Spada, E. Zabalza, A. Lesarri, F. J. Basterretxea, J. A. Fernández, W. Caminati, E. J. Cocinero, *Phys. Chem. Chem. Phys.* **18**, 3966–3974 (2016).

²¹ J.-U. Grabow, S. Mata, J. L. Alonso, I. Peña, S. Blanco, J. C. López, C. Cabezas, *Phys. Chem. Chem. Phys.* **13**, 21063–21069 (2011).

²² S. P. Dempster, O. Sukhorukov, Q.-Y. Lei, W. Jäger, *J. Chem. Phys.* **137**, 174303 (2012).

²³ Y. Xu, W. Jäger, *J. Chem. Phys.* **106**, 7968–7980 (1997).

²⁴ G. Sedo, J. van Wijngaarden, *J. Chem. Phys.* **131**, 044303 (2009).

²⁵ L. Evangelisti, G. Sedo, J. van Wijngaarden, *J. Phys. Chem. A* **115**, 685–690 (2011).

²⁶ M. D. Marshall, H. O. Leung, B. Q. Scheetz, J. E. Thaler, J. S. Muenter, *J. Mol. Spectrosc.* **266**, 37–42 (2011).

²⁷ H. O. Leung, D. Gangwani, J.-U. Grabow, *J. Mol. Spectrosc.* **184**, 106–112 (1997).

²⁸ S. L. Stephens and N. R. Walker, *J. Mol. Spectrosc.* **263**, 27–33 (2010).

²⁹ A. R. Hight Walker, W. Chen, S. E. Novick, B. D. Bean, M. D. Marshall, *J. Chem. Phys.* **102**, 7298–7305 (1995).

³⁰ G. S. Grubbs II, C. T. Dewberry, K. C. Etchison, K. E. Kerr, S. A. Cooke, *Rev. Sci. Instrum.* **78**, 096106 (2007).

³¹ D. A. Obenchain, A. A. Elliott, A. L. Steber, R. A. Peebles, S. A. Peebles, C. J. Wurrey, G. A. Guirgis, *J. Mol. Spectrosc.* **261**, 35–40 (2010).

³² J. J. Newby, M. M. Serafin, R. A. Peebles, S. A. Peebles, *Phys. Chem. Chem. Phys.* **7**, 487–492 (2005).

³³ J. R. Avilés Moreno, J. Demaison, T. R. Huet, *J. Am. Chem. Soc.* **128**, 10467 (2006).

³⁴ D. R. Lide, M. Jen, *J. Chem. Phys.* **40**, 252–253 (1964).

³⁵ J. P. Porterfield, S. Eibenberger, D. Patterson, M. C. McCarthy, *Phys. Chem. Chem. Phys.* **20**, 16828 (2018).

³⁶ J. P. Porterfield, J. H. Westerfield, L. Satterthwaite, D. Patterson, P. B. Changala, J. H. Baraban, M. C. McCarthy, *J. Phys. Chem. Lett.* **10**, 1981 (2019).

³⁷ J. F. Kaiser, “Digital Filters” - Ch 7 in “Systems analysis by digital computer”, Editors: F. F. Kuo and J. F. Kaiser, p 218-285. John Wiley and Sons, New York, (1966).

³⁸ H.V.L. Nguyen, I. Kleiner, *Phys. Sci. Rev.* **7**, 679–726 (2022).

³⁹ H.V.L. Nguyen, *J. Phys. Chem. Lett.*, **16**, 104–113 (2024).
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This is the author's peer reviewed, accepted manuscript. However, the online version of record will be different from this version once it has been copyedited and typeset.
PLEASE CITE THIS ARTICLE AS DOI: 10.1063/5.0256434

⁴⁰ T. Nguyen, Structures and Internal Dynamics of Methylated Nitrogen Containing Aromatic Rings Probed by Means of Microwave Spectroscopy, Quantum Chemical Calculation and Spectral Modelling, Université de Paris, France (2021).

⁴¹ H.V.L. Nguyen, W. Caminati, J.-U. Grabow, *Molecules* **27**, 3948 (2022).