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A typical power spectrum of the beat signal of the THz QCL that is phase locked to a microwave reference recorded by the spectrum analyzer with a low resolution bandwidth (RBW) of 100 KHz. For comparison, a spectrum of the free-running QCL is also shown. The inset shows a relative frequency shift of the free-running QCL emission line versus the biasing current at 5 K. The starting frequency is 2.735 THz.  

A typical power spectrum of the beat signal of the THz QCL that is phase locked to a microwave reference recorded by the spectrum analyzer with a low resolution bandwidth (RBW) of 100 KHz. For comparison, a spectrum of the free-running QCL is also shown. The inset shows a relative frequency shift of the free-running QCL emission line versus the biasing current at 5 K. The starting frequency is 2.735 THz.  

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Citations

... For example, this was achieved by mixing the QCL signal with a tone of a subharmonic Schottky diode mixer [5][6][7] or superlattice mixer [8]. Locking to the output of a 1.5 THz and 2.7 THz Schottky diode frequency multiplier chain (FMC) has also been demonstrated utilizing cryogenic superconducting mixers [9,10]. Optical frequency combs have also been used to lock THz QCLs via the generation of an RF beat note in a photoconductive mixer [11], electrooptic sampling in a ZeTe crystal [12], or a superconducting mixer [13]. ...
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Optical injection locking of a metasurface quantum-cascade (QC) vertical-external-cavity surface-emitting laser (VECSEL) is demonstrated at 2.5 THz using a Schottky diode frequency multiplier chain as the injection source. The spectral properties of the source are transferred to the laser output with a locked linewidth of ∼1 Hz, as measured by a separate subharmonic diode mixer, and a locking bandwidth of ∼300 MHz is achieved. The large locking range is enabled by the microwatt power levels available from modern diode multipliers. The interplay between the injected signal and feedback from external reflections is studied and demonstrated to increase or decrease the locking bandwidth relative to the classic locking range depending on the phase of the feedback.
... Frequency-and phase-locking of ridge wave waveguide THz QCLs has been demonstrated using a variety of techniques including: referencing the QCL to a more stable gas laser or frequency multiplier chain (FMC) source using a superconducting hot electron bolometer [12,13] or diode mixer [14,15], locking to an optical or THz frequency comb [16][17][18], locking to a subharmonic diode mixer with an RF synthesized pump [19,20], direct injection locking with signal from a THz photomixer [21], and locking to a gas cell [22][23][24]. ...
... While it is difficult to directly compare these free running results to those from other studies due to varying setups and measurement techniques, typical free-running linewidths for ridge waveguide THz QCLs have been reported to be 1-10 MHz [12,15,42,43]. As it was established in Section II that the impact of QC-material refractive index on the lasing frequency for the QC-VECSEL should be similar that of a ridge waveguide, the relatively large frequency instability of the QC-VECSEL is suggestive that it is indeed more subject to mechanical instabilities in the external optics than most ridge waveguides. ...
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... Frequency-and phase-locking of ridge wave waveguide THz QCLs has been demonstrated using a variety of techniques including: referencing the QCL to a more stable gas laser or frequency multiplier chain (FMC) source using a superconducting hot electron bolometer [12,13] or diode mixer [14,15], locking to an optical or THz frequency comb [16][17][18], locking to a subharmonic diode mixer with an RF synthesized pump [19,20], direct injection locking with signal from a THz photomixer [21], and locking to a gas cell [22][23][24]. ...
... While it is difficult to directly compare these free running results to those from other studies due to varying setups and measurement techniques, typical free-running linewidths for ridge waveguide THz QCLs have been reported to be 1-10 MHz [12,15,42,43]. As it was established in Section II that the impact of QC-material refractive index on the lasing frequency for the QC-VECSEL should be similar that of a ridge waveguide, the relatively large frequency instability of the QC-VECSEL is suggestive that it is indeed more subject to mechanical instabilities in the external optics than most ridge waveguides. ...
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... This value is considerably smaller than the free-running linewidths of waveguide-based THz QC-lasers, which are typically on the order of a few MHz when measured over times of more than a few seconds and are primarily limited by temperature and current fluctuations. [14][15][16][17] This is expected, since in a QC-VECSEL, most of the cavity mode resides within vacuum and not the QC-active material and, hence, is less sensitive to refractive index fluctuations of the semiconductor. This is consistent with the fact that the tuning coefficient is measured to be 1.7 kHz/mA, which is 3-4 orders of magnitude smaller than that reported for waveguide-based QClasers or even short-cavity VECSELs. ...
... starting point for further stabilization using method such as frequency locking to gas absorption lines 30 or high-finesse optical cavities, 31 and phase-locking to optical frequency combs 32 or harmonics of a microwave frequency standard. 15 However, this comes at the expense of a limited electrical frequency tuning range; future work will be required to combine this approach with frequency agility. ...
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... Frequency converters that can operate at ambient temperatures enable operation for a long lifetime and eliminate the necessity of bulky cryostats. In 2009, Khosropanah et al. demonstrated phase locking of a 2.7-THz QCL using a superlattice mixer [10]. Later in 2013, Hayton et al. [11] reported both, frequency and phase, locking of a 3.4-THz QCL to a ×15-harmonic signal generated by a superlattice harmonic mixer operating at room temperature. ...
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... The Schottky diode has also been applied as a frequency mixer for producing the RF beat signal from ν THz up to 2.9 THz [22,23]. On the other hand, a semiconductor-superlattice electron device (SLED) with negative differential conductivity at room temperature, which was predicted by Esaki and Tsu in the early 1970s [24], has been demonstrated for THzwave generation [25][26][27] and THz-frequency downconversion [28][29][30] while competing with the Schottky diode. The SLED is a compact, easy-to-use, and room-temperature operational device. ...
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... The intrinsic linewidth of the terahertz QCL is of the order of a few hundreds of Hz [26,27] but thermal, electric, and mechanical instabilities typically result in free-running linewidths of a few MHz [28]. This has led to the development of several techniques to stabilize the frequency of QCLs, including locking to a gas absorption line [29], a multiplied microwave source [30], femtosecond laser frequency combs [31,32], and a femtosecond frequency comb stabilized to a primary frequency reference [33]. All of these methods only make use of an electrical feedback to stabilize the frequency of the QCL to a stable reference source. ...
... Furthermore, the combination of both locking schemes allows us to maintain lower phase error at low frequencies via the electronic PLL, while the addition of terahertz injection provides a wider locking range [34]. Hence, the combined implementation of the terahertz injection phase lock loop (IPLL) provides improved tracking of environmental fluctuations and low phase error variance compared to systems that use either IL [35] or only the electronic PLL configuration [29][30][31][32]. ...
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... Furthermore, SSLs host rich dynamics in the presence of a driving field, which include the formation of Stark ladders [19], the manifestation of Bragg reflections and Bloch oscillations [20]. From the viewpoint of applications, SSLs have attracted great interest because they allow the development of devices which operate at microwave [21] and far-infrared frequencies [5,21] suitable for high precision spectroscopic studies and detection of submillimeter waves. In addition, a considerable number of studies have tackled the task of engineering parametric amplifiers [22,23] and frequency multipliers [24,25,26] based on superlattice periodic structures. ...
... Furthermore, SSLs host rich dynamics in the presence of a driving field, which include the formation of Stark ladders [19], the manifestation of Bragg reflections and Bloch oscillations [20]. From the viewpoint of applications, SSLs have attracted great interest because they allow the development of devices which operate at microwave [21] and far-infrared frequencies [5,21] suitable for high precision spectroscopic studies and detection of submillimeter waves. In addition, a considerable number of studies have tackled the task of engineering parametric amplifiers [22,23] and frequency multipliers [24,25,26] based on superlattice periodic structures. ...
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Semiconductor superlattices are strongly nonlinear media offering several technological challenges associated with the generation of high-frequency Gigahertz radiation and very effective frequency multiplication up to several Terahertzs. However, charge accumulation, traps and interface defects lead to pronounced asymmetries in the nonlinear current flow, from which high harmonic generation stems. This problem requires a full non-perturbative solution of asymmetric current flow under irradiation, which we deliver in this paper within the Boltzmann-Bloch approach. We investigate the nonlinear output on both frequency and time domains and demonstrate a significant enhancement of even harmonics by tuning the interface quality. Moreover, we find that increasing arbitrarily the input power is not a solution for high nonlinear output, in contrast with materials described by conventional susceptibilities. There is a complex combination of asymmetry and power values leading to maximum high harmonic generation.
... Furthermore, SSLs host rich dynamics in the presence of a driving field, which include the formation of Stark ladders [21], the man- * mauro.pereira@ku.ac.ae ifestation of Bragg reflections and Bloch oscillations [22]. From the viewpoint of applications, SSLs have attracted great interest because they allow the development of devices which operate at microwave [23] and far-infrared frequencies [5,23] suitable for high precision spectroscopic studies and detection of submillimeter waves. In addition, a considerable number of studies have tackled the task of engineering parametric amplifiers [24,25] and frequency multipliers [26][27][28] based on superlattice periodic structures. ...
... Furthermore, SSLs host rich dynamics in the presence of a driving field, which include the formation of Stark ladders [21], the man- * mauro.pereira@ku.ac.ae ifestation of Bragg reflections and Bloch oscillations [22]. From the viewpoint of applications, SSLs have attracted great interest because they allow the development of devices which operate at microwave [23] and far-infrared frequencies [5,23] suitable for high precision spectroscopic studies and detection of submillimeter waves. In addition, a considerable number of studies have tackled the task of engineering parametric amplifiers [24,25] and frequency multipliers [26][27][28] based on superlattice periodic structures. ...
Preprint
In this paper we solve the Boltzmann-Bloch equation within a path integral approach, delivering general, non-perturbative solutions of high harmonic generation in semiconductor superlattices with asymmetric current flow. The system is treated non-perturbatively in the illuminating field by employing local boundary conditions which allow the inclusion of asymmetric relaxation rates. The spectroscopic properties of the high harmonic generation are demonstrated by calculations of the nonlinear response in both frequency and time domain. We show that asymmetric currents affect the spontaneous emission and can result in a significant enhancement of even harmonics by tuning the interface quality.