Gradient refractive index liquid crystal optical apparatus and image display apparatus

A gradient index liquid crystal optical apparatus comprising:

• a first substrate including a principal plane;
• a second substrate;
• a liquid crystal layer disposed between the principal plane of the first substrate and the second substrate;
• a first electrode, a second electrode, a third electrode, and a fourth electrode arranged in a first direction that is parallel to the principal plane between the principal plane and the liquid crystal layer;
• a fifth electrode, a sixth electrode, a seventh electrode, and an eighth electrode arranged in the first direction between the principal plane and the liquid crystal layer, the fifth electrode at least partially overlapping the first electrode when projected on the principal plane, the sixth electrode at least partially overlapping the second electrode when projected on the principal plane, the seventh electrode at least partially overlapping the third electrode when projected on the principal plane, and the eighth electrode at least partially overlapping the fourth electrode when projected on the principal plane;
• a ninth electrode and a tenth electrode disposed between the principal plane and the liquid crystal layer, the ninth electrode being located between the fifth electrode and the sixth electrode when projected on the principal plane, and the tenth electrode being located between the seventh electrode and the eighth electrode when projected on the principal plane;
• dielectric layers disposed between the first electrode and the fifth electrode, between the second electrode and the sixth electrode, between the third electrode and the seventh electrode, and between the fourth electrode and the eighth electrode;
• and
• an eleventh electrode disposed between the second substrate and the liquid crystal layer,
• a minimum distance between the fifth electrode and the ninth electrode projected on the principal plane being less than a minimum distance between the first electrode and the ninth electrode projected on the principal plane, a minimum distance between the sixth electrode and the ninth electrode projected on the principal plane being less than a minimum distance between the second electrode and the ninth electrode projected on the principal plane, a minimum distance between the seventh electrode and the tenth electrode projected on the principal plane being less than a minimum distance between the third electrode and the tenth electrode projected on the principal plane, a minimum distance between the eighth electrode and the tenth electrode projected on the principal plane being less than a minimum distance between the fourth electrode and the tenth electrode projected on the principal plane,
• a minimum distance between the sixth electrode and the third electrode projected on the principal plane being greater than a minimum distance between the second electrode and the third electrode projected on the principal plane, and a minimum distance between the seventh electrode and the second electrode projected on the principal plane being greater than the minimum distance between the third electrode and the second electrode projected on the principal plane.