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Summary

We describe the generation of far-infrared radiation using an optically pumped molecular laser along with the measurement of their frequencies with heterodyne techniques. The experimental system and techniques are demonstrated using difluoromethane (CH₂F₂) as the laser medium whose results include three new laser emissions and eight measured laser frequencies.

Abstract

The generation and subsequent measurement of far-infrared radiation has found numerous applications in high-resolution spectroscopy, radio astronomy, and Terahertz imaging. For about 45 years, the generation of coherent, far-infrared radiation has been accomplished using the optically pumped molecular laser. Once far-infrared laser radiation is detected, the frequencies of these laser emissions are measured using a three-laser heterodyne technique. With this technique, the unknown frequency from the optically pumped molecular laser is mixed with the difference frequency between two stabilized, infrared reference frequencies. These reference frequencies are generated by independent carbon dioxide lasers, each stabilized using the fluorescence signal from an external, low pressure reference cell. The resulting beat between the known and unknown laser frequencies is monitored by a metal-insulator-metal point contact diode detector whose output is observed on a spectrum analyzer. The beat frequency between these laser emissions is subsequently measured and combined with the known reference frequencies to extrapolate the unknown far-infrared laser frequency. The resulting one-sigma fractional uncertainty for laser frequencies measured with this technique is ± 5 parts in 10⁷. Accurately determining the frequency of far-infrared laser emissions is critical as they are often used as a reference for other measurements, as in the high-resolution spectroscopic investigations of free radicals using laser magnetic resonance. As part of this investigation, difluoromethane, CH₂F₂, was used as the far-infrared laser medium. In all, eight far-infrared laser frequencies were measured for the first time with frequencies ranging from 0.359 to 1.273 THz. Three of these laser emissions were discovered during this investigation and are reported with their optimal operating pressure, polarization with respect to the CO₂ pump laser, and strength.

Introduction

The measurement of far-infrared laser frequencies was first performed by Hocker and co-workers in 1967. They measured the frequencies for the 311 and 337 μm emissions from the direct-discharge hydrogen cyanide laser by mixing them with high order harmonics of a microwave signal in a silicon diode¹. To measure higher frequencies, a chain of lasers and harmonic mixing devices were used to generate the laser harmonics². Eventually two stabilized carbon dioxide (CO₂) lasers were chosen to synthesize the necessary difference frequencies^3,4. Today, far-infrared laser frequencies up to 4 THz can be measured with this technique using only the first harmonic of the difference frequency generated by two stabilized CO₂ reference lasers. Higher frequency laser emissions can also be measured using the second harmonic, such as the 9 THz laser emissions from the methanol isotopologues CHD₂OH and CH₃¹⁸OH.^5,6 Over the years, the accurate measurement of laser frequencies has impacted a number of scientific experiments^7,8 and permitted the adoption of a new definition of the meter by the General Conference of Weights and Measures in Paris in 1983.^9–11

Heterodyne techniques, such as those described, have been immensely beneficial in the measurement of far-infrared laser frequencies generated by optically pumped molecular lasers. Since the discovery of the optically pumped molecular laser by Chang and Bridges¹², thousands of optically pumped far-infrared laser emissions have been generated with a variety of laser media. For example, difluoromethane (CH₂F₂) and its isotopologues generate over 250 laser emissions when optically pumped by a CO₂ laser. Their wavelengths range from approximately 95.6 to 1714.1 μm.^13–15 Nearly 75% of these laser emissions have had their frequencies measured while several have been spectroscopically assigned^16–18.

These lasers, and their accurately measured frequencies, have played a crucial role in the advancement of high-resolution spectroscopy. They provide important information for infrared spectral studies of the laser gases. Often these laser frequencies are used to verify the analysis of infrared and far-infrared spectra because they provide connections among the excited vibrational state levels that are often directly inaccessible from absorption spectra¹⁹. They also serve as the primary radiation source for studies investigating transient, short-lived free radicals with the laser magnetic resonance technique²⁰. With this extremely sensitive technique, rotational and ro-vibrational Zeeman spectra in paramagnetic atoms, molecules, and molecular ions can be recorded and analyzed along with the ability to investigate the reaction rates used to create these free radicals.

In this work, an optically pumped molecular laser, shown in Figure 1, has been used to generate far-infrared laser radiation from difluoromethane. This system consists of a continuous wave (cw) CO₂ pump laser and a far-infrared laser cavity. A mirror internal to the far-infrared laser cavity redirects the CO₂ laser radiation down the polished copper tube, undergoing twenty six reflections before terminating at the end of the cavity, scattering any remaining pump radiation. Therefore the far-infrared laser medium is excited using a transverse pumping geometry. To generate laser action, several variables are adjusted, some simultaneously, and all are subsequently optimized once laser radiation is observed.

In this experiment, far-infrared laser radiation is monitored by a metal-insulator-metal (MIM) point contact diode detector. The MIM diode detector has been used for laser frequency measurements since 1969.^21–23 In laser frequency measurements, the MIM diode detector is a harmonic mixer between two or more radiation sources incident on the diode. The MIM diode detector consists of a sharpened Tungsten wire contacting an optically polished Nickel base²⁴. The Nickel base has a naturally occurring thin oxide layer that is the insulating layer.

Once a laser emission was detected, its wavelength, polarization, strength, and optimized operating pressure were recorded while its frequency was measured using the three-laser heterodyne technique^25–27 following the method originally described in Ref. 4. Figure 2 shows the optically pumped molecular laser with two additional cw CO₂ reference lasers having independent frequency stabilization systems that utilize the Lamb dip in the 4.3 μm fluorescence signal from an external, low pressure reference cell²⁸. This manuscript outlines the process used to search for far-infrared laser emissions as well as the method for estimating their wavelength and in accurately determining their frequency. Specifics regarding the three-laser heterodyne technique as well as the various components and operating parameters of the system can be found in Supplemental Table A along with references 4, 25–27, 29, and 30.

Protocol

1. Planning of Experiments Conduct a survey of the literature to assess prior work performed using the laser medium of interest, which for this experiment is CH2F2. Identify all known laser emissions along with all information about the lines such as their wavelength and frequency. Several surveys of known laser emissions are available13,31–37. Compile all spectroscopic investigations of the molecule used as the laser medium with a focus on prior Fourier transform34 and optoacoustic studies38,39. 2. Generating Far-Infrared Laser Emissions Safety Overview. Develop a standard operating procedure for the lab that includes proper eye protection when working with the CO2 and far-infrared laser systems. Alignment and Calibration. Calibrate each CO2 laser using a grating-based spectrum analyzer designed for the CO2 laser according to the manufacturer’s protocol. Align the end mirrors and the coupling mirror in the far-infrared laser cavity using a He-Ne laser so that their radiation is focused onto the MIM diode detector. Direct the radiation from the CO2 pump laser into the far-infrared laser cavity through a sodium chloride window at an angle of approximately 72o with respect to the cavity axis. Direct the radiation from the two CO2 reference lasers to either their respective low-pressure fluorescence reference cell or co-linearly onto the MIM diode detector using beam splitters and additional mirrors. Detection of far-infrared laser radiation. Polish the Nickel base every several days using a standard metal polish. Crimp a 25 μm tungsten wire into a copper post and bend the wire into the configuration shown in Figure 3. Adjust the length of the wire so that it is between 10 to 20 wavelengths of the radiation being measured. Electrochemically etch the tip of the wire in a saturated sodium hydroxide (NaOH) solution by applying a voltage (approximately 3.5 to 5 VAC) to the solution. Re-etch the tip with a low voltage (less than 1 VAC). This roughens the tip of the wire and improves the diode’s performance. Rinse the wire with distilled water. Insert the copper post into the MIM diode’s housing once the wire is dry. Place the wire in contact with the Nickel base using a fine screw and level system. Contacts yielding a resistance across the diode between 100 and 500 Ω are typically used when detecting and measuring far-infrared laser radiation. Generation of far-infrared laser radiation. Set the CO2 pump laser on a specific laser emission, e.g., 9P36. Rotate the micrometer dial on the CO2 pump laser back and forth to achieve maximum intensity on the beam stop. Adjust the tilt of the CO2 pump laser’s grating to achieve maximum intensity on the beam stop. Repeat steps 2.4.2 and 2.4.3 until the output power for the CO2 pump laser appears optimized on the beam stop. Remove the beam stop from the path of the CO2 pump laser. Turn on and align the optical chopper into the beam path of the CO2 pump laser. Open the valve on the CH2F2 cylinder to introduce the far-infrared laser medium into the far-infrared laser cavity. Adjust the metering valve on the inlet line until a pressure of approximately 10 Pa is achieved. Note: Only the approximate pressure is necessary since it is used as a way of systematically scanning the far-infrared laser cavity. Set the position of the output coupler such that its outermost tip is approximately 1 cm from the middle of the laser cavity as indicated by a calibrated scale on the outside of the laser cavity. Note: Only the approximate location is necessary since it is used as a way of systematically scanning the far-infrared laser cavity. Adjust the position of the moveable far-infrared laser mirror in approximately 0.25 mm increments by rotating the calibrated micrometer dial back and forth. Simultaneously tune the frequency of the CO2 pump laser through its gain curve by changing the voltage applied across the CO2 pump laser’s piezoelectric transducer (PZT). If no signal is observed on the oscilloscope display, repeat step 2.4.10 with the output coupler moved to its next position where the tip is approximately 1.5 cm from the middle of the laser cavity as indicated by a calibrated scale on the outside of the laser cavity. If no signal is observed on the oscilloscope display, repeat step 2.4.10 with the output coupler moved to its next position where the tip is approximately 2 cm from the middle of the laser cavity as indicated by a calibrated scale on the outside of the laser cavity. If no signal is observed on the oscilloscope display, repeat steps 2.4.9 through 2.4.12 with a far-infrared laser pressure of approximately 19 Pa as adjusted with the metering valve on the inlet line. If no signal is observed on the oscilloscope display, repeat steps 2.4.9 through 2.4.12 with a far-infrared laser pressure of approximately 27 Pa as adjusted with the metering valve on the inlet line. If no signal is observed on the oscilloscope display, insert the beam stop into the path of the CO2 pump laser and close the valve on the CH2F2 cylinder until the far-infrared laser pressure is approximately 0 Pa. Set the CO2 pump laser to the next laser emission, e.g., 9P34, and optimize the output power using steps 2.4.2 through 2.4.4. Repeat steps 2.4.5 through 2.4.16 until all emissions generated by the CO2 pump laser are used. When searching for far-infrared laser lines, place a focus on CO2 pump laser emissions whose frequencies overlap with any absorption regions identified in step 1.2. Characterizing far-infrared laser emissions. Simultaneously adjust the pressure of the far-infrared laser medium, the voltage applied to the CO2 pump laser’s PZT, and the position of the output coupler until the far-infrared laser emission’s output power is maximized (determined by a maximum peak-to-peak signal from the MIM diode detector as observed on the oscilloscope display, similar to Figure 4). Turn the micrometer dial clockwise until the far-infrared laser emission is observed on the oscilloscope display. Record the position of the micrometer dial. Turn the micrometer dial clockwise for an additional 20 modes corresponding to the same far-infrared laser emission. Record the position of the micrometer dial. Subtract the position of the micrometer dial in steps 2.5.2 and 2.5.3. Divide this difference by 10 to obtain the wavelength of the far-infrared laser emission. Repeat steps 2.5.2 through 2.5.4 a total of five times and average the wavelength of the far-infrared laser emission. Average laser wavelengths measured by traversing at least 20 adjacent longitudinal modes have a one-sigma uncertainty of ± 0.5 μm. Measure the polarization of the far-infrared laser radiation, relative to the CO2 pump radiation, using either a gold wire-grid polarizer (394 lines/cm) or a Brewster polarizer. 3. Determining Far-Infrared Laser Frequencies Identifying the CO2 reference laser emissions. Calculate the frequency of the far-infrared laser emission based on its measured wavelength. Identify sets of CO2 reference laser lines whose frequency difference is within several GHz of the calculated frequency for the far-infrared laser emission40. A typical list used for such measurements is shown in Table 1. Searching for the heterodyne beat signal. Identify the first set of CO2 reference laser lines and set each CO2 reference laser on their respective laser emission. Optimize the output power for each CO2 reference laser using steps 2.4.2 through 2.4.4 and the monitor power meter. Adjust an iris, either internal or external to each reference laser, so that the power from each CO2 reference laser is approximately 100 mW as measured by the monitor power meter shown in Figure 2. Block the radiation from the CO2 pump laser using a beam stop while unblocking the radiation from the CO2 reference lasers. Turn on and align the optical chopper into the co-linear beam path of the CO2 reference lasers. Optimize for maximum peak-to-peak voltage each CO2 reference laser emission on the MIM diode detector using several mirrors, beam splitters, and a 2.54 cm focal length ZnSe plano-convex lens while observing the output on the oscilloscope, similar to Figure 5. Block the radiation from the CO2 reference lasers using a beam stop while unblocking the radiation from the CO2 pump laser. Re-optimize the CO2 pump laser and the far-infrared laser, as necessary, so that the far-infrared laser emission has a maximum peak-to-peak voltage as observed on the oscilloscope. Disconnect the MIM diode detector’s output from the oscilloscope and connect it to an amplifier whose output is observed on a spectrum analyzer. Unblock the radiation from the CO2 reference lasers. Remove the optical choppers modulating the CO2 pump and reference lasers. Set the spectrum analyzer on a 40 MHz span and search for the beat signal in 1.5 GHz increments by manually scanning this frequency range using the spectrum analyzer’s adjustment knob. If no beat signal is observed, disconnect the MIM diode’s output from the amplifier and connect it to the oscilloscope. Block the radiation from the CO2 reference lasers and reinsert the optical chopper into the path of the CO2 pump laser. Repeat steps 3.2.2 through 3.2.13 as necessary until the spectrum analyzer has been used to search for the beat signal between 0 and 12 GHz. If no beat signal is observed, repeat steps 3.2.2 through 3.2.14 with another set of CO2 reference laser lines until either the beat signal is observed or all possible sets of CO2 reference laser lines are exhausted. Stabilizing the CO2 reference frequencies. Apply a voltage between 0 and 900 V to the first CO2 reference laser’s PZT so that the signal from its respective fluorescence reference cell is at the center of the Lamb dip, illustrated in Figure 6 and as viewed on an oscilloscope as in Figure 7. Activate the feedback voltage applied to the first CO2 reference laser’s PZT using a custom built lock-in/servo amplifier so that it remains locked to the center of the Lamb dip. Repeat steps 3.3.1 and 3.3.2 for the second CO2 reference laser. Visually monitor the output of the pre-amp on an oscilloscope, as in Figure 7, to ensure the reference lasers remains locked. Measurement of the beat frequency. Center the beat signal on the spectrum analyzer display and adjust its amplitude to maximize its size on the display. Set the spectrum analyzer to view two simultaneous traces of the beat signal, as in Figure 8, by selecting the Clear Write feature for both Trace 1 and Trace 2. One trace will display the instantaneous signal while the other will record the maximum signal (using a Max Hold feature on the spectrum analyzer for the second trace). Rotate the micrometer dial on the far-infrared laser cavity back and forth across the gain curve for a given cavity mode. Use the View feature on the spectrum analyzer to freeze the second (Max Hold) trace once a symmetric pattern is obtained. Slightly rotate the micrometer dial clockwise to decrease the length of the far-infrared laser cavity. Simultaneously observe the subsequent small shift in the beat frequency on the spectrum analyzer due to this slight increase in the frequency of the far-infrared laser. Place markers at the full width at half maximum points of the symmetric pattern (Max Hold trace) using the Marker function with the Delta feature on the spectrum analyzer. Measure the center frequency of the beat signal using the Span Pair feature on the spectrum analyzer. Repeat steps 3.4.1 through 3.4.7. Disengage the lock in/servo amplifier for each CO2 reference laser to unlock each laser from its center frequency and re-optimize each CO2 reference laser. Re-lock the reference lasers using steps 3.3.1 through 3.3.4. Repeat steps 3.4.1 through 3.4.10 for a total of 6 measurements. Once complete, unlock each CO2 reference laser from its center frequency. Calculate the revised frequency of the far-infrared laser emission using these beat frequencies to obtain an accurate prediction for the second set of CO2 reference laser lines. Identify a different set of CO2 reference laser lines whose frequency difference is within several GHz of the calculated frequency for the far-infrared laser emission. Optimize the next set of CO2 reference laser lines on the MIM diode detector and obtain the beat signal using steps 3.2.2 through 3.2.15 as necessary. Lock the new set of CO2 reference laser lines using steps 3.3.1 through 3.3.4. Repeat steps 3.4.1 through 3.4.10 for a total of 6 measurements. Once complete, unlock each CO2 reference laser from its center frequency. Insert beam stops into the paths of the CO2 pump and reference lasers. Calculation of the far-infrared laser frequency. Calculate the unknown far-infrared laser frequency, νFIR, using the measured beat frequency through the relation                                                    FIR = |νCO2(I)–νCO2(II)| ± |νbeat|                               Eq. 1 where |νCO2(I)–νCO2(II)| is the magnitude of the difference frequency synthesized by the two CO2 reference lasers and |νbeat| is the magnitude of the beat frequency. The ± sign in Eq. 1 is determined experimentally from step 3.4.5. Obtain an average frequency and calculate the uncertainty.

Representative Results

As mentioned, the frequency reported for a far-infrared laser emission is an average of at least twelve measurements performed with at least two different sets of CO2 reference laser lines. Table 2 outlines the data recorded for the 235.5 μm laser emission when using the 9P04 CO2 pump laser. For this far-infrared laser emission, fourteen individual measurements of the beat frequency were recorded. The first set of measurements were recorded while using the 9R1…

Discussion

There are several critical steps within the protocol that require some additional discussion. When measuring the far-infrared laser wavelength, as outlined in step 2.5.3, it is important to ensure the same mode of the far-infrared laser emission is being used. Multiple modes of a far-infrared laser wavelength (i.e., TEM₀₀, TEM₀₁, etc.) can be generated within the laser cavity and thus it is important to identify the appropriate adjacent cavity modes being used to measure the wavelength^…

Materials

Vacuum pump	Leybold	Trivac D4A	HE-175 oil; Quantity = 3
Vacuum pump	Leybold	Trivac D8B or D16B	Fomblin Fluid; Quantity = 1 of each
Vacuum pump	Leybold	Trivac D25B	HE-175 oil; Quantity = 1
Optical chopper with controller	Stanford Research Systems	SR540
Lock-in amplifier	Stanford Research Systems	SR830
Spectrum analyzer	Agilent	E4407B	ESA-E Series, 9 kHz to 26.5 GHz Spectrum Analyzer
Amplifier 	Miteq	AFS-44	Provides amplification of signals between 2 and 18 GHz. The amplifier is powered by a Hewlett Packard triple output DC power supply, model E3630A.
Amplifier 	Avantek	AWL-1200B	Provides amplification of signals less than 1.2 GHz.
Power supply	Hewlett Packard	E3630A	Low voltage DC power supply for amplifier.
Power supply	Glassman	KL Series	High voltage power supply for the CO<sub>2</sub> lasers; Quantity = 2; negative polarity
Power supply	Fluke	412B	High voltage power supply used with the NIST Asymmetric HV Amp
Detector	Judson Infrared Inc	J10D	For fluorescence cell; Quantity = 2
CO<sub>2</sub> laser spectrum analyzer	Optical Engineering&nbsp;	16-A	Currently sold by Macken Instruments Inc.
Thermal imaging plates with UV light	Optical Engineering&nbsp;		Primarily used for aligning the CO<sub>2</sub> reference lasers. Currently sold by Macken Instruments Inc.
Resistors	Ohmite&nbsp;	L225J100K	100 kW, 225 W. Between 4 to 6 resistors are used in each ballast system. Each CO<sub>2</sub> laser has its own ballast system. Fans are used to cool the resistors.
HV relay, SPDT	CII Technologies	H-17	Quantity = 3; one for each CO<sub>2</sub> laser
Amplifier&nbsp;	Princeton Applied Research	PAR 113	Used with fluorescence cell; Quantity = 2
Oscilloscope	Tektronix	2235A	Similar models are also used; Quantity = 2
Oscilloscope/Differential amplifier	Tektronix	7903 oscilloscope with 7A22 differential amplifier
Power meter with sensor	Coherent	200	For use below 10 W.&nbsp; This is the power meter shown in Figure 2.
Power meter with sensor	Scientech, Inc	Vector S310	For use below 30 W
Multimeter	Fluke	73III	Similar models are also used; Quantity = 3
Data acquisition	National Instruments	NI cDAQ 9174 chassis with NI 9223 input module	Uses LabVIEW software
Simichrome polish	Happich GmbH		Polish for the Nickel base used in the MIM diode detector. Although the Nickel base can be used immediately after polishing, a 12 hour lead time is typically recommended.
Pressure gauge	Wallace and Tiernan	61C-1D-0050	Series 300; for CO<sub>2</sub> laser; Quantity = 3
Pressure gauge with controller	Granville Phillips	Series 375	For far-infrared laser
Zirconium Oxide felt	Zircar Zirconia	ZYF felt	Used as a beam stop
Zirconium Oxide board	Zircar Zirconia	ZYZ-3 board	Used as a beam stop; Quantity = 4
Teflon sheet	Scientific Commodities, Inc	BB96312-1248	1/32 inch thick; used for the far-infrared laser output window
Polypropylene	C-Line sheet protectors	61003	used for the far-infrared laser output window
Vacuum grease	Apiezon
Power supply	Kepco	NTC 2000	PZT power supply
PZT tube	Morgan Advanced Materials		1 inch length, 1 inch outer diameter, 0.062 inch thickness, reverse polarity (positive voltage on outside); Quantity = 3
ZnSe (AR coated)	II-VI Inc		CO<sub>2</sub> laser window (Quantity = 3), lens, and beam splitter (Quantity 3)
NaCl window	Edmond Optics		Quantity = 1
CaF window	Edmond Optics		Quantity = 2
Laser mirrors and gratings	Hyperfine, Inc		Gold-coated; includes positioning mirrors
Glass laser tubes and reference cells	Allen Scientific Glass
MIM diode detector	Custom Microwave, Inc
Other			Other materials include magnetic bases, base plates, base clamps, XYZ translation stage, etc.