Patent ID: 7388822

Claim:
A liquid crystal lens element having a variable focal length, comprising: a pair of transparent substrates each provided with a transparent electrode, voltage application means for applying voltage between the respective transparent electrodes provided on the pair of substrates, a concave-convex portion made of a transparent material and having a cross-section of saw-tooth shape or a cross-section of saw-tooth shape approximated by steps, that have rotational symmetry about an optical axis of the liquid crystal lens element, and formed on one of the transparent electrodes, and a liquid crystal filling at least concave portions of the concave-convex portion, wherein a substantial refractive index of the liquid crystal is changed according to the magnitude of the voltage applied between the transparent electrodes by the voltage application means, the liquid crystal has an ordinary refractive index n o and an extraordinary refractive index n e (here, n o ≠n e ), the substantial refractive index of the liquid crystal layer changes within a range of from n o to n e according to the magnitude of the applied voltage, alignment direction of liquid crystal molecules at no voltage application is uniformly in a specific direction in the liquid crystal layer, and the transparent material of the concave-convex portion is a transparent material having a refractive index n s at least for extraordinarily polarized incident light, and the refractive index n s is a value between n o and n e (not containing cases where the value n s equals to n o or n e ), and the transparent material of the concave-convex portion has a refractive index n s satisfying the following formula: | n e −n s |≦|n e −n o |/2 and the concave-convex portion has concave portions having a depth d within the following formula at a wavelength λ of light transmitted through the liquid crystal: ( m− 0.25) ·λ/|n e −n s |≦d≦ ( m+ 0.25) ·λ/|n e −n s | wherein m=1, 2 or 3 and m determines a number of switchable focal lengths of the liquid crystal lens element.