Switchable liquid crystal fresnel lens

A liquid crystal Fresnel lens, comprising:

• a liquid crystal cell, comprising:
• two transparent substrates having conducting layers and at least one photoalignment layer disposed thereon, wherein the at least one photoalignment layer includes multiple alignment domains in a Fresnel zones pattern, and wherein easy axes of adjacent alignment domains of the Fresnel zones pattern are oriented at an angle relative to one another;
• a ferroelectric liquid crystal layer disposed between the two transparent substrates, wherein the ferroelectric liquid crystal layer has a planar surface orientation and smectic layers perpendicular to the two transparent substrates, and
• wherein the ferroelectric liquid crystal layer comprises electrically-suppressed helix ferroelectric liquid crystals with helix pitch smaller than the thickness of the ferroelectric crystal layer;
• and
• a voltage source, configured to apply an AC rectangular voltage to the conducting layers with amplitude higher than the critical voltage amplitude for helix unwinding of the electrically-suppressed helix ferroelectric liquid crystals so as to facilitate switching the liquid crystal cell between different states;
• and
• two polarizers, wherein the liquid crystal cell is disposed between the two polarizers;
• and
• wherein zone boundaries of the Fresnel zones pattern are approximately defined by circles having radii according to the formula
• r
• n
• =
• n
• ⁢
• ⁢
• λ
• ⁢
• ⁢
• f
• +
• n
• 2
• ⁢
• λ
• 2
• 4
• where n is an integer, λ is a wavelength of light, and f is a focal length of the liquid crystal Fresnel lens.