Phase locking of two coupled lasers with many longitudinal modes

Abstract

Detailed experimental and theoretical investigations on two coupled fiber lasers, each with many longitudinal modes, reveal that the behavior of the longitudinal modes depends on both the coupling strength as well as the detuning between them. For low to moderate coupling strength only longitudinal modes which are common for both lasers phase-lock while those that are not common gradually disappear. For larger coupling strengths, the longitudinal modes that are not common reappear and phase-lock. When the coupling strength approaches unity the coupled lasers behave as a single long cavity with correspondingly denser longitudinal modes. Finally, we show that the gradual increase in phase-locking as a function of the coupling strength results from competition between phase-locked and non phase-locked longitudinal modes. c 2018 Optical Society of America Phase locking of two coupled lasers operating with only one longitudinal mode was investigated over the years [1][2][3][4]. It was shown theoretically and experimentally that a simple relation exist between the coupling strength that is needed for phase locking and the frequency detuning between the lasers [4][5][6]. While a sharp transition from no phase locking to full phase locking when the coupling strength exceeds a critical value is predicted, the experimental results revealed a gradual transition, which could be explained by introducing noise to each laser [4,6]. For lasers with many longitudinal modes it was shown that for strong coupling strength only common longitudinal modes survive, leading to full phase locking [7][8][9][10]. Yet, the detailed behavior of phase locking and the spectrum of longitudinal modes as a function of the coupling strength between coupled lasers were so far not reported.Here we present our investigations and results on two coupled fiber lasers, each operating with up to 20,000 longitudinal modes. Specifically, we show how the phase locking between the two lasers and their longitudinal mode spectrum vary as a function of the coupling strength which is continually and accurately controlled with polarization elements. We find a gradual increase in the number of longitudinal modes which are phase locked as the coupling strength increases, leading to a gradual transition from no phase locking to full phase locking without the need to introduce noise. We support the experimental results with calculations in which a modified effective reflectivity model is exploited.The experimental configuration for determining the phase locking and the spectrum of longitudinal modes for two coupled fiber lasers as a function of the coupling strength between them is presented in Fig. 1. Each fiber laser was comprised of a polarization maintaining Ytterbium doped fiber, where one end was attached to a high reflection fiber Bragg grating (FBG), with a central wavelength of 1064nm and a bandwidth of about 1nm, that served as a back reflector mirror, the other end attached to a collimating graded index (GRIN) lens with anti-reflection coating to suppress a...

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