Optical system and image display device

An optical system comprising:

• a light guide for guiding an image light ray which is output from a display element and forms an image, to a field of view region of a user as a virtual image,
• wherein:
• the light guide includes a body having a plate shape, and an in-coupling region and an exit region which are defined in the body;
• the in-coupling region is configured to:
• (i) divide the image light ray incident from the display element into a plurality of image light rays in first, second, and third branch directions intersecting each other;
• and (ii) allow the plurality of image light rays to propagate within the body;
• the exit region is configured to allow at least one of the plurality of image light rays propagating within the body to emerge from the body toward the field of view region;
• the in-coupling region includes a periodic structure constituted by recessed or protruded parts in relation to a thickness direction of the body which are arranged to have periodicity in three predetermined directions parallel to the first, second, and third branch directions, respectively, within a predetermined plane perpendicular to the thickness direction of the body;
• central axes of the recessed or protruded parts are inclined relative to the thickness direction of the body in each of:
• (i) a plane including the second branch direction and the thickness direction of the body;
• and (ii) a plane including the third branch direction and the thickness direction of the body;
• and
• a ratio of a size of the recessed or protruded parts relative to a period of arrangement of the recessed or protruded parts is larger in a direction perpendicular to the first branch direction within the predetermined plane than in a direction perpendicular to the second branch direction within the predetermined plane and a direction perpendicular to the third branch direction within the predetermined plane.