Frequency comb for THz metrology and spectroscopy

First, the photomixing experiment we have developed at the LPCA during the last decade is presented on figure 1. This spectrometer is able to work between 300 and 3000 GHz with a frequency accuracy and a THz frequency linewidth suitable for high resolution THz spectroscopy [1-2]. The photomixing process is known from long time, and consist to convert an optical beat note into the THz domains. It is one of the best approach to cover a large part of the THz frequency gap. Thus, the frequency of the THz radiation produced is just the difference frequency of the two lasers working around 750 nm (and corresponding to a frequency around 400 THz) required to use of photomixer made in LTG GaAs. In principle, the frequency accuracy of the radiated THz radiation depends of the frequency accuracy of the pumps lasers. Clearly, there are no commercial solution to reach a precision better than 100 kHz often required for high resolution rotational spectroscopy. An alternative way consists to use a FC produce by a femtosecond laser as a ruler to control and to measure the difference frequency between the two pump lasers. In the present demonstration, the FC is produced by a frequency doubled erbium doped modelocked fiber laser with a stabilized repetition rate around 100 MHz. A beatnote between the laser and the nearest FC mode was isolated and phase locked to a local oscillator coherently locking the diode to the FC. The locking of the second laser to a different FC mode allows the difference frequency between the pump lasers to be synthesized. Feedback correction signal is applied to control the difference frequency of pump laser, and thus the THz frequency. The difference of frequency between the diode lasers can be expressed in Eq. (1) as:

Frequency combs (FC) have radically changed the landscape of frequency metrology and highresolution spectroscopy investigations extending tremendously the achievable resolution while increasing signal to noise ratio. By describing two experiments, we highlight that like other spectral ranges, THz domain can exploit a frequency comb.
First, the photomixing experiment we have developed at the LPCA during the last decade is presented on figure 1. This spectrometer is able to work between 300 and 3000 GHz with a frequency accuracy and a THz frequency linewidth suitable for high resolution THz spectroscopy [1][2]. The photomixing process is known from long time, and consist to convert an optical beat note into the THz domains. It is one of the best approach to cover a large part of the THz frequency gap. Thus, the frequency of the THz radiation produced is just the difference frequency of the two lasers working around 750 nm (and corresponding to a frequency around 400 THz) required to use of photomixer made in LTG GaAs. In principle, the frequency accuracy of the radiated THz radiation depends of the frequency accuracy of the pumps lasers. Clearly, there are no commercial solution to reach a precision better than 100 kHz often required for high resolution rotational spectroscopy. An alternative way consists to use a FC produce by a femtosecond laser as a ruler to control and to measure the difference frequency between the two pump lasers. In the present demonstration, the FC is produced by a frequency doubled erbium doped modelocked fiber laser with a stabilized repetition rate around 100 MHz. A beatnote between the laser and the nearest FC mode was isolated and phase locked to a local oscillator coherently locking the diode to the FC. The locking of the second laser to a different FC mode allows the difference frequency between the pump lasers to be synthesized. Feedback correction signal is applied to control the difference frequency of pump laser, and thus the THz frequency. The difference of frequency between the diode lasers can be expressed in Eq. (1) as: where ! "" is the repetition rate of the femtosecond laser, n is an integer, and ! " is the frequency of the synthesizer used to phase lock the beat signals against synthesizer to a precise frequency control. A classical commercial wavemeter is used to remove the ambiguity of the integer.
Various species have been study by use of this spectrometer from highly polar molecules (OCS, H 2 CO) up to low and non-polar (CH 3 D, CH 4 ) compounds and as well as radicals (OH, SO) to cite a fews [3][4][5][6].
Top Ultra LowNoise Oscillators from Wenzel). f s is the frequency of the synthesizer used to phase lock the beat signals, and the quantity ( ± f s ± f s ) is subsequently named offset frequency. A classical commercial wavemeter is used to remove the ambiguty of the integer. The need to determine the carrier envelope offset (CEO) frequency introduced into the laser cavity has limited the use of FC techniques, however in our case as the ECDL difference frequency is required the measurement of the CEO is avoided. Fig. 1. Experimental setup of the synthesised THz source. A first beam splitter (BS1) is used to overlap the two laser beams from the two External Cavity Diode Laser (ECDL) and seed them to Tapered Amplifier (TA). At the output, optical beat note is divided by a second beam splitter (BS2). A first part is used to produce the THz radiation collected at the backside of the photomixer by a silicon lens. Two Off axis Parabolic Mirrors (OPM) are used to collimate and focus the THz beam through an absorption cell to a cryogenic bolometer. The frequency comb (FC) is overlap with optical beat note by means of a third beam splitter (BS3). Two grating (G) disperse the FC and two lasers to ensure an heterodyne measurement between each ECDL and FC detected by two different photodiodes (PD1-PD2). The heterodyne signals are feed to two Phase Lock Loop (PLL) to synthesized the difference frequency between two ECDL to a synthesizer. A 10 MHz crystal oscillator is used as reference signal for synthesizers, counters and spectrum analyzers required. Solids lines show optical signal, and dashed lines indicate electronic signal.

Measurements onto THz synthesizer
The frequency accuracy and the stability of the repetition rate is measured and checked by use of a counter, also referenced to the same 10 MHz reference oscillator. A frequency repetition rate around 100 MHz associated with a standard deviation of 5 × 10 −3 Hz for a gate time of 1s and for a measurement time of 18 minutes was routinely obtained. Similar measurements of the two beat notes between ECDL and FC signal typically yielded mean values around 20 MHz associated with standard deviations of 2 Hz. An example of a locked beat note between one of the diode lasers and a FC mode and associated frequency histogram measurement are shown in Fig. 2 and Fig. 3 respectively. The absolute frequency accuracy of the THz synthesizer is then determined by the accuracy of the 10 MHz reference oscillator. In these preliminary experiments, a commercial frequency counter calibrated against Cs etalon is used to check the reference oscillator. The full width of the beat note, shows on Fig. 2, at −3dB is less than 100 kHz and represents the convolution of the ECDL and FC linewidths which currently exhibit broader optical comb lines than those of Ti:Sa based comb generator [17]. Experimental setup of the THz photomixing spectrometer. BS1 is a beam splitter to overlap the two laser beams from the two External Cavity Diode Laser (ECDL) and seed Tapered Amplifier (TA). Then, the optical beat note is divided by a second beam splitter (BS2) to produce THz radiation and to manage the THz frequency. BS3 is used to overlap optical beat note and the frequency comb. Two grating (G) disperse the FC and the two lasers to ensure a heterodyne analysis between each ECDL and a part of FC thank to photodiodes (PD1 and PD2). The heterodyne signals are used to control the frequency of each laser.
Second, a very popular approach for THz investigations is the well-known THz Time Domain Spectrometer. Except the dual comb approach, the discrete spectral properties of the generated radiation which forms a THz offset free frequency comb is often ignored. However, the exploitation of the frequency comb structure of THz pulses should lead to an exceptional frequency resolution. To explore this approach, a dedicated heterodyne detection has been implemented around 200 GHz in order to analyse at very high resolution the THz FC (figure 2). Knowing exactly the repetition rate of the femtosecond laser used to produce the THz FC and intermediate frequency thanks to spectrum analyser, different components of the THz FC can be identified without ambiguity (figure 3). By tuning the repetition rate and/or the frequency of the local oscillator, high resolution spectroscopy can be performed [7].
Those two examples show the potential of the Frequency Comb to improve spectroscopic investigations in the THz domain.