Continuous-wave terahertz system with electro-optical terahertz phase control T. Go¨bel, D. Schoenherr, C. Sydlo, M. Feiginov, P. Meissner and H.L. Hartnagel A method of electro-optical control of the terahertz (THz) phase in con- tinuous-wave photomixing THz systems is suggested and demon- strated. The method enables phase-sensitive detection without any moving mechanical components in the system. Additionally, the method allows lock-in detection without a mechanical chopper, which increases the signal-to-noise ratio of the system. Introduction: Photomixing terahertz (THz) systems, both short-pulse and continuous-wave (CW) ones, have the advantages of wide spectral coverage and phase-sensitive detection with high signal-to-noise ratio (SNR) [1]. The combination of such properties in one THz system is hardly achievable with other approaches, rather than photomixing. Additionally, the CW systems allow one to achieve high spectral resol- ution [2]. Therefore, photomixing systems have become quite common in recent years. Variable delays (typically realised with large mechanical delay stages) are unavoidable in such systems for photoconductive/ electro-optic detection. Such delay stages prevent the realisation of the optical part of the systems all-in-fibre, they are the obstacles to making the systems stable and reliable. In the case of short-pulse photo- mixing systems, the problem could be circumvented by the use of two lasers with slightly different repetition rates in one system [3]. In the case of CW photomixing systems, the problem has not been resolved till now. The demonstration of a solution is the objective of this Letter. Conventional CW-system configuration: The schematic of a standard CW THz system [1, 2, 4, 5] is shown in Fig. 1. The system has two lasers with slightly different frequencies v 1 and v 2 . Their radiation is mixed together by a beam combiner (beam splitter). Since the frequen- cies of the lasers are adjacent, an optical beat note appears in both beams after the combiner, i.e. the optical power in those two beams is modu- lated at the difference frequency of the lasers (Dv, where Dv ¼ jv 1 2 v 2 j). One beam illuminates the photoconductive or electro-optic emitter (Tx) of the THz radiation and the second beam illuminates the detector (Rx) [4]. The detected current (I det DC ) in the system can be rep- resented in the form I DC det / cos f THz  Dvd c þ f syst   ð1Þ where f THz is the phase shift accumulated in the THz part of the system, d is the additional delay length introduced by the delay stage and c is the velocity of light. The phase shift in the system due to the path length difference of the two optical branches is denoted by f syst . To determine the phase and amplitude of the detected THz signal, it is necessary to scan the delay stage over the length of minimum one THz wavelength (c/Dv). If the lowest frequency of the system is 100 GHz, then the delay should be at least 3 mm. The resolution of the delay stage is deter- mined by the highest THz frequency of the system. If it is around a few THz, then the delay stage should have the resolution of at least several micrometres. Such requirements can be realised in practice only by a mechanical one. The delay stage can be introduced either in the optical part of the system [1, 2, 4, 5] or in the THz one (as in Fig. 1). mechanical delay stage beam combiner Rx Tx chopper laser 1, 1 laser 2, 2 Fig. 1 Conventional CW THz system with photomixers In the latter case, the optical part can be realised in fibre but one has to cope with distortions of the THz beam and a variation of the THz path due to the delay stage, which can cause significant errors. The use of a mechanical delay stage also limits the measurement speed; the acqui- sition time for a single frequency point can amount to several seconds owing to the limited travelling velocity of the translation stage. Thus, broadband frequency sweeps with high resolution result in extremely long measurement times for conventional setup configurations. For the required lock-in detection, either a mechanical chopper should be included (i) into the optical part of the system or (ii) into the THz one (as in Fig. 1) or (iii) the DC bias of THz emitter has to be modulated. The disadvantage of the first two options is that a bulky mechanical chopper has to be used. The drawback of options (i) and (iii) is that either the DC current, DC voltage or temperature of the emitting photomixer are una- voidably modulated at the lock-in frequency. This creates a parasitic radiation/distortion that can be picked up by the detector. This parasitic signal can appear as an additional DC THz-phase-independent back- ground in the detected signal [5] or as an additional noise. phase modulator laser 1, 1 laser 2, 2 Rx Tx mod splitter combiner Fig. 2 Modified CW THz system Optical phase modulator replaces both mechanical delay stage and chopper Modified CW-system configuration: The idea of the modified system is the following: the phase shift of f mod (by an optical phase modulator) of one of the optical beams before the beam combiner results in the phase shift of the whole beat note (its envelope function) by the same phase f mod . Therefore the need for a large (mechanical) delay stage is elim- inated. The schematic of the modified system is shown in Fig. 2. After simple algebra, one can show that the detected current in the modified configuration is I DC det / cos f THz  f mod þ f syst   ð2Þ Here, f THz is dependent on Dv and f syst is a function of the individual wavelengths of the lasers. In principle, f syst or (depending on the tar- geted application) the combination f THz þf syst could be set to zero by the proper balancing of the different lengths in the system. Hence, (2) shows that the optical phase shift of f mod is equivalent to the phase shift of the same value in the THz part of the system. Thus, the need for a large mechanical delay stage is eliminated, since only the optical phase has to be modulated. The required optical delay length of the phase modulator is on the order of the optical wavelength (’1 mm) for any Dv. The phase delay of the phase modulator required to achieve a given phase shift of the THz wave is independent of the THz (or even GHz or MHz) frequency of the system, which facilitates the system implementation. A further advantage of the optical phase modulator is the possibility of using it instead of a chopper. One can add an additional phase modu- lation ( f chop ) to f mod : f mod ! f mod þ f chop , where f chop is changing stepwise between 0 and p at the lock-in frequency. That changes step- wise the sign of the detected current I DC det at the same frequency and allows the realisation of the lock-in detection. This approach is free from the disadvantages of the conventional systems above. It keeps the average optical power on emitter and receiver constant, and neither DC current, DC voltage nor temperature of the THz emitter are modu- lated. Thus, no corresponding parasitic signal influences the detected current, reducing the noise level in the detected current. Further, the detected signal is twice as large as in the case of a mechanical chopper. Experimental verification: For experimental proof of our concept, we realised a two-colour laser system, as shown in Fig. 2. For the sake of low-cost implementation, we arranged the optical mixing part in free- space technique. After the individual beams are combined, the optical beat signals are coupled to single-mode fibres, which are connected to the photomixers. As optical source, two distributed feedback (DFB) diode lasers are applied. They operate at a wavelength of around 780 nm and can be tuned in frequency via temperature. As THz emitter and receiver, low-temperature-grown GaAs based photomixers are used [4]. The employed electro-optic phase modulator (Leysop EM400L) with a voltage amplifier features a maximum modulation ELECTRONICS LETTERS 3rd July 2008 Vol. 44 No. 14