Use an image as the texture for a lamp. (See Avoid distortions when creating projector effect)
and add volume scatter to the world (or create a mesh around the scene as voume scatter domain) so that the beam becomes visible.
Click on the image to enlarge.
A way to create this effect is to use blurred object motion.
- Add a curve to the scene that the laser need to follow.
- Add an empty. Add a constraint to the empty to follow the animated curve path. This empty will be a target for the laser.
- Add a plane.
- Add a thin cylinder that will act as the laser.
- In edit mode, create a vertex group for the bottom of the cylinder. This vertex group will follow the target.
- Add a hook modifier to the cylinder. Set the target to the empty used for the laser target. Set the vertex group on the bottom of the cylinder.
- Add a small sphere. This will illuminate the floor. When done, it should resemble something like this Setup blur
- In the Render Properties panel enable blur and set the number of frames to blur. See this question for more details - Is it possible to simulate a long exposure shot in Blender?
8. For the cylinder and sphere, on the Object Properties panel, enable motion blur, enable deformation, and set the steps to 7. 9. Shade the cylinder and sphere with an emissive shader. The brightness can be adjusted using film exposure or emission strength. 10. Render!