We propose and analyze designs for stationary and compact optical concentrators. The designs are based on a catadioptric assembly with a linear focus line. They have a focal distance of around 10 to 15 cm with a concentration ratio (4.5 to 5.9 times). The concentrator employs an internal linear-tracking mechanism, making it suitable for rooftop solar applications. The optical performance of the collector has been simulated with ray tracing software (Zemax), and laser-based indoor experiments were carried out to validate this model. The results show that the system is capable of achieving an average optical efficiency of around 66% to 69% during the middle 6 (sunniest) h of the day. The design process and principles described in this work will help enable a new class of rooftop solar thermal concentrators.