# Two-Color TeraHertz Radiation by a Multi-Pass FEL Oscillator
## 1 Introduction  
TeraHertz (THz) radiation is a frontier research area in physics, chemistry, medicine, and biological and material sciences. The increasing number of advanced and exciting applications of THz waves in all these fields demands versatile and tunable sources combining high-power and excellent output performances. Traditional microwave sources in the THz region, like backward wave oscillators, oortons, vircators, and klimotons suffer from simple physical scaling problems, metallic wall losses, the need for higher static magnetic, electric fields, and electron current densities with increasing frequency, and have already achieved saturation in their developments. A summary of these sources and their main properties can be found in [1]. Other sources, like IMPATT-diodes, are low-cost, reliable, and compact, but characterized by moderately efficient mW power levels. THz sources of high quality are scarce, this lack being often referred to in the literature as the 'THz gap'. Considerable efforts have been put towards the development of novel sources of THz radiation and the aforementioned gap has recently begun to be filled by a wide choice of new technologies capable of generating high-power and tunable radiation. In particular, the THz range of the electromagnetic spectrum can be covered by Free-Electron Lasers (FELs), whose widely tunable radiation shows optimal performances in terms of pulse energy stability, polarization, and spectrum and spatial distribution in this domain. The key parameters of several operating FELs with an exhaustive comparative analysis can be found in [2]. The THz FELs in operation produce coherent radiation characterized by very short pulse lengths and up to MW-level peak intra-cavity powers with continuously tunable wavelengths from 10 \(\upmu\)m to 0.2 mm. The THz wave is now available in both the continuous wave (CW) and the pulsed form, down to single cycles or less. Mainly, infrared (IR) and far-IR FELs are designed to operate as oscillators, that is, they are equipped with resonators confined by metal-coated mirrors [3], one of which is translucent or contains outcoupling apertures for radiation extraction. Some of the advantages of the FEL oscillator mode with respect to other FEL configurations, like single-pass FELs operating in Self-Amplified Spontaneous Emission (SASE), seeded, or superradiant modes, are its compactness, the relaxed requirements for the electron bunch quality, and the factthat oscillators are suitable for super-conducting linacs enabling the generation of powerful quasi-CW light. Few devices exploiting this scheme operate worldwide [4, 5, 6] or have been proposed [7, 8]. Similar to the multi-pass FEL oscillator configuration is the storage-ring FEL oscillator [9], where the electron beam circulating in the storage ring participates in the FEL interaction during each pass through a FEL undulator. The envisioned applications of such a source include high-repetition-rate pump-probe experiments and investigation of reactions with very small quantum yield [10]. Two-color operation could widely increase the number and the interest of the applications. A pioneering experiment for the production of two-color far Infrared-THz radiation has been shown in the Ref. [11]. In particular, IR pump-THz probe configuration can elucidate phenomena such as the response of low-frequency collective solvent modes in liquids, and transient photoconductivity in a variety of semiconductor systems, such as bulk GaAs, low-temperature grown GaAs, nanocrystalline colloidal TiO\({}_{2}\), and CdSe quantum dots. Other specific measurements instead need a Terahertz pump-Terahertz probe scheme. In this paper, we show that the electron beam produced by a super-conducting linac (as, for instance, the one described in [12]), driven in a sequence of two undulator modules of different periods, can generate two-color Terahertz radiation with wavelengths ranging from 100 \(\upmu\)m to 2 \(\upmu\)m. The two pulses of different wavelengths are synchronized, both MW-class and highly coherent.