An intracavity HeNe birefringent dual-frequency laser is investigated for applications. The substrate of such a laser cavity mirror is made of quartz crystal instead of ordinary optical glass. The surface that functions as the laser cavity mirror is coated with a high-reflecting thin film layer, while the surface joined to the discharge tube is coated with an antireflecting thin film layer. Thus, the laser is an intracavity laser and the quartz crystal located inside the cavity causes the longitudinal mode to split into two modes (frequencies). To obtain the appropriate design parameters for various frequency differences, a series of quartz crystal cavity mirrors with different cut angles is experimentally investigated. The relationship of mode splitting and the cut angle are observed. To estimate the splitting by one mirror for different cavity lengths, the following concepts are presented: relative mode (frequency) splitting (ration of mode splitting versus longitudinal mode spacing) and relative optical path difference (ration of optical path difference versus half-wavelength).