Optical system and image display device

1 . 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;

wave vectors in the first, second, and third branch directions are denoted by k1, k2, and k3, respectively:

a maximum value of absolute values |k1|, |k2|, |k3| of the wave vectors in the first, second, and third branch directions is denoted by |km|; and

the wave vectors k1, k2, and k3 satisfy a relation of |k1−k2+k3|<|km|/5.

2 . The optical system according to claim 1 , wherein

central axes of the recessed or protruded parts are inclined relative to the thickness direction of the body.

3 . The optical system according to claim 2 , wherein

inclined angles of the recessed or protruded parts relative to the thickness direction of the body are larger than 20 degrees and smaller than 65 degrees.

4 . The optical system according to claim 1 , wherein

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.

5 . The optical system according to claim 4 , wherein;

the in-coupling region is on a surface of the body on which the image light ray is configured to be incident; and

the central axes of the recessed or protruded parts are inclined:

in a direction opposite from the second branch direction, relative to a direction of the surface of the body on which the image light ray is configured to be incident, in the plane including the second branch direction and the thickness direction of the body; and

in a direction opposite from the third branch direction, relative to the direction of the surface of the body on which the image light ray is configured to be incident, in the plane including the third branch direction and the thickness direction of the body.

6 . The optical system according to claim 4 , wherein:

the in-coupling region is on a surface of the body from which the at least one of the plurality of image light rays is configured to emerge; and

the central axes of the recessed or protruded parts are inclined:

in the second branch direction, relative to a direction of the surface of the body from which the at least one of the plurality of image light rays is configured to emerge, in the plane including the second branch direction and the thickness direction of the body; and

in the third branch direction, relative to the direction of the surface of the body from which the at least one of the plurality of image light rays is configured to emerge, in the plane including the third branch direction and the thickness direction of the body.

7 . The optical system according to claim 4 , wherein

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.

8 . The optical system according to claim 1 , wherein:

the in-coupling region is configured to divide the image light ray incident from the display element into the plurality of image light rays in the first, second, and third branch directions and a fourth branch direction; and

a wave vector in the fourth branch direction is denoted by k4, and k4 is equal to −k1.

9 . The optical system according to claim 1 , wherein the absolute values |k1|, |k2|, |k3| of the wave vectors in the first, second, and third branch directions are identical to each other.

10 . The optical system according to claim 1 , wherein

the absolute values |k1|, |k2|, |k3| of the wave vectors in the first, second, and third branch directions are different from each other.

11 . The optical system according to claim 1 , wherein:

the exit region includes the periodic structure; and

the periodic structure of the in-coupling region and the periodic structure of the exit region have a same period in each of the three predetermined directions.

12 . The optical system according to claim 1 , wherein

the recessed or protruded parts are arranged within the predetermined plane in a hexagonal lattice.

13 . The optical system according to claim 1 , wherein

the light guide is configured to reproduce a pupil of the image right ray to expand the pupil by: dividing the image light ray entering the light guide from the in-coupling region into a plurality of mutually parallel image light rays in each of the three predetermined directions to be allowed to emerge toward the field of view region.

14 . The optical system according to claim 1 , further comprising:

a projection optical system configured to allow the image light ray to be incident on the in-coupling region of the light guide as a collimate light ray.

15 . An image display device comprising:

the optical system according to claim 1 ; and

the display element.

16 . 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.