Interest in the exploration of, and the establishment of a human settlement, on Mars is rapidly growing. To accomplish this, rapid transit will be required to bring important supplies and cargo. Current missions to Mars take at least 150 days, which would be too long in case of emergencies or urgent needs. Therefore, we propose the use of a cutting-edge technology that could allow transit times as short as 20 days: laser energy driven light sails. This propulsion method uses a ground-based laser array to propel a small, lightweight spacecraft attached to a light sail to very high speeds, enabling missions that are much faster than current missions. By utilizing a MATLAB model and a laser propulsion computational tool, we visualize and determine the optimal trajectories and departure windows for these missions. We discuss these trajectories and show that these missions are possible during specific launch windows within a 27-month time period between 2030-2032, but have practical challenges within this period as well. During solar conjunction, such rapid transit missions are limited due to the proximity of the sun, but rapid transits are possible during all orbital phases when the transit time requirement is relaxed. Laser arrays capable of generating up to 13 GW are necessary to enable 20day missions with a 5 kg spacecraft, capable of carrying valuable lightweight cargo to astronauts, near conjunction, but only 0.55 GW is required around opposition. Required spacecraft velocities always exceed the solar system escape velocity and the trajectories are hyperbolic. A significant challenge for future work involves mechanisms and processes for deceleration and entry, descent, and landing. A ground-based laser array on Mars could address some aspects of this challenge, but orbital geometry limits deceleration potential, implying that payloads would need to be robust to large deceleration and impact gloads. These 20-day missions to Mars can serve as precursors to more complex, distant missions. Spacecraft mass capabilities can be increased while also decreasing transit times by optimizing the laser array and light sail properties. Multiple spacecraft may also be launched and boosted simultaneously to carry more payload and decrease costs. This work is intended to serve as a proof of concept that lightweight payloads can be transported via such missions. Technologies enabling rapid transit missions can be developed in the next several decades and be applied to deep space missions to other celestial bodies and journeys to interstellar space.