A frequency tunable terahertz heterodyne spectrometer, based on a third-order distributed feedback quantum cascade laser as a local oscillator, has been demonstrated by measuring molecular spectral lines of methanol ͑CH 3 OH͒ gas at 3.5 THz. By varying the bias voltage of the laser, we achieved a tuning range of ϳ1 GHz of the lasing frequency, within which the molecular spectral lines were recorded. The measured spectra show excellent agreement with modeled ones. By fitting we derived the lasing frequency for each bias voltage accurately. The ultimate performance of the receiver including the resolution of noise temperature and frequency is also addressed. © 2011 American Institute of Physics. ͓doi:10.1063/1.3599518͔Driven by the demands of astronomical observations and atmospheric remote sensing in the terahertz ͑THz͒ frequency range, we have recently developed a high resolution heterodyne spectrometer using a quantum cascade laser ͑QCL͒ at 2.9 THz as a local oscillator ͑LO͒ and a NbN hot electron bolometer ͑HEB͒ as a mixer.1 However, such a spectrometeris not yet adequate for operation in a telescope because of a number of drawbacks noted during the previous experiment. First, the QCL used previously was based on a metal-metal waveguide Fabry-Perot cavity design, which has no mode control of the lasing frequency and has virtually zero tuning range by the bias voltage because of a resulting strong reduction in the output power. The tuning capability is, in general, highly desirable for application in spectroscopy as it is crucial for targeting more molecular lines, and also a means to identify unknown spectral lines when a heterodyne receiver is operated in the double sideband ͑DSB͒ mode. 1 Second, a 4 He flow cryostat was used to operate the QCL. For any balloon-borne and space mission, the use of a liquid-He based cryostat can impose a serious obstacle due to the relatively high DC power dissipation of the laser. Therefore, a dry, liquid cryogen-free cooler such as a pulse tube cryocooler or a Stirling cooler 2 is preferred. One of the challenges in using a dry cooler is the mechanical stability. As demonstrated in Ref. 3, the vibration in the cooler can introduce deviations in the operating point of the detector, leading to instability of the receiver.In this letter we report on a high-resolution heterodyne molecular spectroscopic experiment applying a 3.5 THz QCL as a LO. In comparison with the previous work, 1 there are three key differences; ͑a͒ a single mode, third-order distributed feedback ͑DFB͒, tunable QCL ͑Refs. 4 and 5͒ is used as a LO; ͑b͒ a pulse tube cryocooler is applied to operate the QCL; and ͑c͒ a theoretical model for methanol molecular lines has been verified at 3.5 THz, which was not possible until now because of the lack of a heterodyne technique at such a frequency. By using the third-order periodic structure with strong refractive index contrast gratings, not only is the single mode emission achieved in the DFB laser, but also the radiation power out-coupling from the laser to the free...