The birefringence He-Ne dual-frequency laser (DFL) has so far provided only frequency differences (FDs) larger than 40 MHz, as a result of mode suppression (competition) between the two frequencies. This paper reports experiments on mode suppression in cavity tuning and demonstrates an approach to eliminate this suppression in order to generate small FD ranging from 3 MHz to hundreds of megahertz in birefringence He-Ne DFLs. This is realized with two intracavity elements: a calcite plate and a quartz crystal plate. The calcite plate is used to separate the paths of a light and e light spatially, in parallel, in the laser core of about 1-mm diam, so that light of each polarization acquires gain from its own group of active atoms without mode suppression. Also, the quartz plate is used to precisely tune the magnitude of the FD. This work has filled in the gap of FD between 3 and 40 MHz, which neither traditional Zeeman nor birefringence He-Ne DFLs can supply
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