We demonstrate for the first time the closure of an electronic phase lock loop for a continuous–wave quantum cascade laser (QCL) at 1.5 THz. The QCL is operated in a closed cycle cryo cooler. We achieved a frequency stability of better than 100 Hz, limited by the resolution bandwidth of the spectrum analyser. The PLL electronics make use of the intermediate frequency (IF) obtained from a hot electron bolometer (HEB) which is downconverted to a PLL IF of 125 MHz. The coarse selection of the longitudinal mode and the fine tuning is achieved via the bias voltage of the QCL. Within a QCL cavity mode, the free-running QCL shows frequency fluctuations of about 5 MHz, which the PLL circuit is able to control via the Stark–shift of the QCL gain material. Temperature dependent tuning is shown to be nonlinear, and of the order of -16 MHz/K. Additionally we have used the QCL as local oscillator (LO) to pump an HEB and perform, again for the first time at 1.5 THz, a heterodyne experiment, and obtain a receiver noise temperature of 1741K.
©2009 Optical Society of America
Quantum cascade lasers  (QCL) have been demonstrated for more than a decade in the IR-regime and the push for longer wavelengths has given rise of laser sources which even cover the Terahertz frequency range . It has been proposed for several years to use QCLs as local oscillators for heterodyne receivers. Recently, the Tunable Heterodyne Infrared Spectrometer (THIS) has successfully demonstrated astronomical observations at 10 μm wavelength using a QCL local oscillator. And only now, since continuous wave operation of THz-QCLs can be achieved with tolerable cooling effort, one might consider THz-QCLs as a practical, sufficiently controllable radiation source for heterodyne receivers.
Heterodyne receivers up to about 1.5 THz  or 2 THz have demonstrated the use of solid state multiplier chains as local oscillators. At higher frequencies, only optically pumped gas lasers[6, 7], limited to selected, fixed frequency operation, or multiplied Backward-Wave-Oscillator sources, limited to a narrow tuning range, have demonstrated successful operation. From the astrophysics side, there is a strong demand for high spectral resolution observations (ν/∆ν > 106) throughout the far-infrared and mid-infrared spectral regime, which houses, among other important spectral signatures, the brightest cooling lines of the dense interstellar medium ([CII] 158 μm, [OI] 63 and 145 μm) and the ground rotational lines of molecular hydrogen at 17 and 28 μm.
The Stratospheric Observatory for Infrared Astronomy  (SOFIA), carrying a 3m-class telescope into the stratosphere at 12 to 14 km observing altitude, will open the sky throughout this wavelength regime. Rapid progress in the detector technology provides sensitive THz-mixers [6, 10] and advanced opto-mechanical designs nowadays allow the realization of moderate size heterodyne arrays for astronomical applications[11, 12]. Given the recent advances in the field, QCLs thus bear the potential to satisfy the strong demand for broadband tunable, high-power, frequency stable radiation sources as local oscillators, necessary to design and implement THz-heterodyne receivers for astronomy.
Previously, experiments with QCLs have been either demonstrations of phase–locking  or usage as local–oscillator source [13, 14], but not both at the same time. In this paper, we report on an important step towards realizing this goal, namely the demonstration of a phase locked QCL operating at 1.5 THz and its use a the local oscillator source in a heterodyne receiver.
The structure of this paper is as follows: In section 2 we describe the experimental setup of the heterodyne receiver demonstration. Section 3 contains the measurements and their interpretations, and finally section 4 we conclude the findings and give an outlook on what we assume to be the next steps towards a practical receiver for submillimeter astronomy.
2. Experimental setup
Our experimental setup makes use of the already existing astrophysical heterodyne receiver CONDOR  which has been developed and built at KOSMA as a principal investigator instrument for highest frequency ground based observations at the Atacama Pathfinder EXperiment  (APEX) telescope.
The CONDOR receiver , a HEB mixer in a cryostat with a pulse tube cooler, comprises a combined cryogenic and warm quasi–optical path. The cryogenic optics consists of a corrugated feed horn that forms a Gaussian beam towards a collimating ellipsoidal mirror, and an infrared and optical blocker. The warm optics are the cryostat window, a Martin–Puplett diplexer for a low–loss overlay of the LO radiation on the RF signal (astronomical signal). The standard CONDOR LO, a computer controlled solid state multiplier chain by Virginia Diodes Inc. (VDI, hereafter VDI–LO), is used to pump the HEB. As a basis oscillator to drive the VDI multiplier chain, we used a YIG oscillator built in–house.
On one hand, we have used the CONDOR receiver in its standard configuration to observe and characterize the phase-locked QCL. In a second experiment, we have replaced the standard LO of CONDOR by the QCL and have verified unchanged sensitivity of the heterodyne experiment with this new LO source.
The QCL in this experiment is one device of a series produced at University of Neuchâtel [16, 17], Switzerland, which demonstrated the successful operation of low frequency terahertz quantum lasers covering the range of 1.2–1.8 THz. This particular device has been integrated in a cryostat which is cooled down to about 4 K by a Balzers closed–cycle cryo cooler. It is a metal–metal waveguide  device with cleaved facets on both sides of the active region, with no additional treatments of the radiating surfaces applied, as described by Walther .
The setup as depicted in Fig. 1 shows a top–view sketch of the optical bench with the beam path indicated. The QCL’s radiation was coupled in through the sky signal port (Port 1) while maintaining the CONDOR local oscillator (LO) in place (Port 2) for reference. To modulate the QCL’s intensity, a rotatable polarizer grid was introduced in the beam path.
The experiments are split in three stages:
2.1. Observation of the QCL emission as sky signal
Here the QCL emission line is observed with CONDOR in its standard receiver configuration. In this case the VDI–LO was used on port 2 in Fig. 1, and the intermediate frequency (IF) output of the receiver was analyzed with either a spectrum analyzer, for longer term integration, or an acousto–optical spectrometer (AOS ) for data dumps on short timescales of the order of 10ms. We observe the QCL laser emission at three longitudinal modes, and verify the tuning capability within such a single, longitudinal mode.
2.2. Temperature–dependent tuning
QCLs change their emission frequency depending on the resonance condition of the modes in the device. Mainly driven by the longitudinal mode structure, the frequency depends on the cavity length and the index of refraction of the lasing material. At cryogenic temperatures of few tens of Kelvin (here TQCL ≈ 20 – 30K) we do not expect any significant length variation of the geometrical cavity length. Therefore, temperature–dependent variation of the index of refraction is the most prominent effect. An additional resistive heater was mounted on the cold head of the QCL cryostat, and the temperature could be raised from 21.9 K with the dissipation of only the QCL, to 29.1 K.
2.3. Phase–locking the QCL with the down–converted CONDOR IF
Phase locking a monochromatic radiation source requires both measuring and adjusting the phase of the source. In our experiment, we are using the IF of the CONDOR receiver (see section 2.1 and Fig. 2) with a frequency down–converter. That allows us to drive a PLL circuit to control the bias voltage of the QCL. In this experiment, we down–convert the IF signal to 200 MHz, feed it into a PLL circuit, and herewith lock the phase of the QCL. Fig. 2 shows the details. The box labeled “PLL” in Fig. 2 is a circuit with a standard phase comparator chip which derives the anaolg control voltage from the phase difference to the reference oscillator.
2.4. QCL as LO for CONDOR
In this stage we configured port 2 in Fig. 1 to be the input for the sky signal. This, together with a free–running QCL on port 1 –serving as LO– is an alternative receiver configuration, and allows us to obtain the figures of merit, e.g. noise temperature of the receiver system, via the Y–factor method, when pumped by the QCL as local oscillator. This method assumes separability of the whole system’s noise into receiver noise and the noise received by the antenna: Tsys = Trec + Ta. With two temperature baths at Thot and Tcold at the antenna input, we isolate and determine Trec.
Note that at a frequency of 1.5 THz, i.e. hν/k = 72K, we are already far off the validity regime of the Rayleigh-Jeans approximation (hν ≪ kT), so that the physical temperatures of the radiation sources have to be explicitely converted to the equivalent brightness temperatures on the commonly used radiation temperature scale Tr = λ 2/2kBν(T) = hν/k1/(e hν/KT - 1) = 𝒥ν(𝓣) This gives radiation temperature for the 300 K hot load and the 77 K cold load of respectively Thot,r = 265K and Tcold,r = 46.5K. The noise powers measured for the two load temperatures are Phot = kB∆ν(Thot,r + Trec) and Pcold = kB∆ν(Tcold,r + Trec), where kB is the Boltzmann constant and ∆ν is the frequency band width of the noise power measurement.
HEB mixers are known to be sensitive to power level fluctuations of the LO, which arise from amplitude modulation of the LO itself, coupling modulation between the LO and HEB due to vibrations, or standing waves in the LO-HEB cavity that get worse with increased coupling between the LO and the HEB. This 1.5 THz–QCL, however, has been characterized to yield a single mode CW power of 300 μW  which would be way too much to pump a single HEB. Hence, from the fact that we are able to just overpump the mixer (flat, all-ohmic I–V curve, see Fig. 4 d), we conclude that we don’t couple in all the power that is available. From the optical setup which has potential for improvement, we estimate that we only couple one percent or less into the mixer. Although the beam pattern has not been assessed in this experiment, a plausible explanation could be that the device might not exhibit a clean beam pattern, similar to the one discussed by Adam et al. . Therefore a possible standing wave amplitude is reasonably low, should it be caused by cavity length modulation, and amplitude modulation due to the QCL itself or vibrations in the mechanical setup are more likely.
3.1. Observation of the QCL emission as sky signal
The QCL was operated under a bias condition af typically 4.4 V and 0.7 A, exhibiting a heat dissipation of about 3 W. A spectrum analyzer (HP8569B) measurement with an integration time of 30s shows a linewidth (FWHM) of 15 MHz (Fig. 3 a). When observed with the AOS on 10ms dump time, the observed linewidth is 1.6 MHz (Fig. 3 b). To verify this long– and short–term behavior, we recorded about 800 AOS dumps of 10 ms integration time with 250 ms dead time in between, and fitted center frequency, amplitude and line width. Fig. 4 shows the results. The scatter of the center frequency of the free–running QCL as seen in the AOS dumps, shown in panel (a) of Fig. 4, is about 7 MHz wide over a time span of about 200s, whereas the spectrum analyzer integration over 30s shows a width of 15 MHz (panel (a) in Fig. 3). These two measurements have been taken at different times throughout the experiment, and it may be caused by changing or developing drift behavior during the time of the experiment.
It is evident, that on short timescales the center frequency of this free–running QCL drifts. The line width, usually around 1.6 MHz, is certainly lower than the scatter of the fitted center frequencies (see panels (a) and (c) in Fig. 4). With a dump frequency of 250 ms we conclude that the effect of the cooling cycle on a frequency shift is negligible since we do not observe any correlated frequency shifts. It is possibly governed by other fluctuations. At a tuning coefficient of around 20 GHz/V, the fitted frequency scatter corresponds to 200μV on the bias voltage.
The lasing modes of the QCL are the longitudinal Fabry-Pérot modes of the cavity. With a cavity length of about 1 mm, the spacing of the Fabry-Pérot modes is about 40 GHz and is large enough compared to the gain curve, so that for most voltages the laser operates in single-mode. Within the tuning range of the CONDOR receiver, it was possible to observe three adjacent modes (1420, 1460 and 1500 GHz) of the QCL, and Fig. 5 shows their measured QCL bias voltage.
The frequency of one longitudinal mode can be tuned by the Stark-shift. The bound-to-continuum design shows a strong blue-shift of the gain curve with the voltage due to the diagonal transition, the so called Stark-shift. This shift alters the value of the complex refraction index, which translates into a shift of frequency of the hot cavity mode, called cavity pulling. Thus by changing the applied voltage, the longitudinal mode can be fine-tuned.
3.2. Temperature–dependent tuning
The longitudinal mode frequency f, or resonance, is described by f = kc/(2nQCLl), where the mode number is given by k, c is the speed of light in the vacuum, nQCL is the effective QCL material index of refraction, and l the length of the cavity. Figure 6 shows this temperature behavior. Obvious temperature dependencies in the above frequency equation are the cavity length, l, and the effective index of refraction , nQCL. We have not made an attempt to quanitify the effect on either of these variables. However, since the operating temperature is of the order of 20 K, the coefficient of linear expansion should be negligible, leaving the temperature dependency of the effective index of refraction as the main contributor to this tuning effect.
3.3. Phase–locking the QCL with the down–converted CONDOR IF
Panel (c) of Fig. 7 shows the 126 MHz PLL monitor signal, resolved with a lowest possible resolution bandwidth of 100Hz. Clearly, in frequency resolution we are here limited by the spectrum analyzer. Now we have obtained a phase–locking of a 1.5 THz–QCL with an accuracy of about 100 Hz. This corresponds to a frequency resolution of ν/∆ν= 1.5·1010.
Since the QCL control bias (voltage and current) are high power signals of several volts at around 1 ampère, it is not straight forward to use the analogue PLL output for controlling the QCL. For better results, low impedance amplifier stage needs to be developed for the future applications.
3.4. QCL as LO for CONDOR
To verify the pump level on the HEB, we used the polarizer in the beam path to attenuate the radiation. The pump levels can be seen in the iv–curves of the HEB in panel (d) of Fig. 4: Since HEBs are bolometric detectors are heated up by the radiation coupled in, the superconduction stops and normal Ohmic behavior is apparent. It shows that we manage to get sufficient power on the HEB: The curve for 0 deg polarizer (maximal power on the HEB) shows that the HEB is fully normally conducting.
Having adjusted the pump level to the optimum operating point of the HEB, we performed a Y-factor calibration which yields the receiver noise temperature Trec: With a hot load at ambient and a cold load at liquid nitrogen temperature, we obtain total power values of the IF output, and the according result as listed in Table 2. The Trec of 1741 K is similar to the noise temperature of receivers at 1.5 THz with a conventional VDI–LO . The QCL therefore does not ad noise to the receiver system.
4. Conclusions and outlook
We have demonstrated phase-locking of a THz–QCL to a frequency-width of below 100 Hz and have shown that this QCL is suitable as local oscillator for a heterodyne receiver. The frequency control via the cavity pulling effect proves to be sufficiently well understood to suppress the frequency fluctuations of a free running QCL with a PLL circuit. Even with replacing the conventional LO with a free running QCL, we have shown that the receiver noise performance does not degrade.
As near-term improvements on the present experimental set-up we are planning to develop an optical bench setup which makes use of the experiences we have in integrated optics design to improve the power coupling efficiency into the receiver. This includes also to integrate both the mixer and the QCL in a single closed–cycle chilled cryostat, with the mixer being coupled to the 4K stage, and the QCL fixed to a 15K or 45K stage, depending on the number of stages of the cryo cooler, to further decrease the QCL’s operating temperature for a larger tunability range.
Additionally we are improving the PLL circuit control stage towards better low–impedance current stability in the sub–milliampère range for appropriate matching to the particular QCL’s bias currents.
The achievements documented in this paper open promising perspectives for the use of QCLs as local oscillator in future array heterodyne receivers in the far-infrared spectral regime on observatory platforms such as the Stratospheric Observatory for Infrared Astronomy SOFIA. An important next step will be to overcome the limitations in the tuning range due to the QCL intrinsic cavity modes. Similar to the experience in our group with the use of QCLs as local oscillators in the THIS–instrument  at IR-wavelength, or by Xu et al. at 4.8 THz , a promising approach here may be via coupling to an external cavity with much larger cavity length, the tuning of which can be used to pull the QCL mode across a wide wavelength range.
This research has been funded by the Deutsche Forschungsgemeinschaft (DFG) through the Collaborative Research Centre SFB494 (Sonderforschungsbereich), the Swiss National Science Foundation (NCCR–Quantum Photonics), and the EU Commission through the IST project “Teranova”.
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