# Superconducting Sub-Terahertz Oscillator with Continuous Frequency Tuning
## 1 Introduction
In this mode, the FFO is characterized by a small value of the electromagnetic wave attenuation parameter \(\alpha\), and the junction operates like a transmission line with well-defined resonant modes of electromagnetic oscillations. Part of the electromagnetic radiation generated by the FFO is reflected from the emitting end of the junction and reaches its opposite side. This results in the occurrence of standing waves in the LJJ at frequencies \(\rm f_{m}=m\pi c_{SW}/L\), where \(\rm m\) is an integer. These modes interact with the Josephson current, and when the frequency of the Josephson current coincides with a frequency of the resonant modes, on the I-V characteristics of the junction steps of the Josephson current at voltages \(\rm V_{m}=m\ h\ c_{SW}/4 eL\), called Fiske steps [31; 32], appear. Thus, the current-voltage characteristics of the LJJ in this voltage range manifest a pronounced resonant structure. This greatly complicates the implementation of smooth tuning of the generator frequency, and even makes it impossible at a constant bias current. At voltage values V\(\rm-V_{g}/3\), a sharp increase in the quasiparticle junction current occurs for an FFO [33], which is explained by the effect of Josephson self-coupling (JSC) [34; 35; 36; 37; 38]. This effect is caused by the energy absorption of high-frequency Josephson radiation generated by the FFO itself by quasiparticles; this leads to the well-known phenomenon of photon-assisted tunneling. The Josephson self-coupling (JSC) effect can be obtained [34; 35] from the Werthamer equation [34]. As a result, the I-V characteristics (IVC) of the FFO show an increase in the quasiparticle current at voltages \(\rm V_{JSC}=V_{g}/(2n+1)\), where \(\rm n\) is an integer, the most pronounced effect is observed at \(\rm n=1\), which corresponds to \(\rm V_{JSC}=V_{g}/3\); as a consequence the attenuation coefficient \(\alpha\) increases significantly. For a tunnel junction of length L, when the condition \(\alpha^{*}\) L/\(\lambda_{\rm J}>1\) is satisfied, the self-pumping effect leads to the disappearance of the Fiske steps and the FFO passes into the so-called flux-flow regime [33]. According to the theory [34; 35], the effect of JSC on the IVC should be more significant for Josephson tunnel junctions with a higher critical current density. The appearance of JSC effect is characterized also by a sharp increase in the differential resistance of the junction at voltages slightly above \(\rm V_{g}/3\). At higher voltages, the differential resistance of the FFO decreases, the autonomous emission linewidth narrows, and it becomes easy to smoothly tune the FFO frequency over a fairly wide range. The FFO generates a signal up to a voltage of the order of \(\rm V_{g}/2=\Delta/e\), as long as the energy of the generated photons does not exceed the energy of the Josephson interaction \(2\Delta\). Photons with higher energies break the Cooper pairs and, therefore, absorption of the electromagnetic wave in the junction electrodes is very high. Figure 1 shows the IVCs of FFOs based on the Nb/Al-AlO\({}_{x}\)/Nb (a) and Nb/Al-AlN/NbN (b) structures, measured at different values of the magnetic field generated by the integrated control line. The pumping current of the SIS mixer, \(\rm I_{pump}\), induced by the FFO radiation (as a percentage of the \(\rm I_{pump}\) to the quasiparticle current jump on the gap voltage, \(\rm I_{g}\)), is depicted by the color. The red areas correspond with the operation parameters of the FFO, at which the \(\rm I_{pump}\) of the SIS mixer exceeds 25% of its current jump at the gap voltage. This level is certainly sufficient for the normal operation of the SIS mixer. The figure clearly shows the boundary of the transition from the resonant mode to the flux-flow mode.