Liquid crystal lens and display device

1. A liquid crystal lens comprising:

a first electrode;

a second electrode disposed opposite to the first electrode; and

a liquid crystal layer, including liquid crystal molecules having refractive anisotropy, disposed between the first electrode and the second electrode, the liquid crystal molecules being changed in alignment depending on voltage applied by the first electrode and the second electrode, thereby to form such a phase difference distribution that phase difference with respect to an incident beam of a fundamental wavelength varies from 0 to 2πβ along the predetermined direction, β being an integer of 2 or more, and to yield such a lens effect that focal lengths for a plurality of incident beams of different wavelengths including the fundamental wavelength are equal to one another,

wherein magnitude of voltage difference between the first electrode and the second electrode is varied in correspondence to the phase difference distribution along the predetermined direction.

2. The liquid crystal lens according to claim 1 , wherein the lens effect by the liquid crystal layer corresponds to a lens effect yielded by a Fresnel-lens.

3. A liquid crystal lens comprising:

a first electrode;

a second electrode disposed opposite to the first electrode; and

a liquid crystal layer, including liquid crystal molecules having refractive anisotropy, disposed between the first electrode and the second electrode, the liquid crystal molecules being changed in alignment depending on voltage applied by the first electrode and the second electrode, thereby to form such a phase difference distribution that phase difference with respect to an incident beam of a fundamental wavelength varies from Q to 2πβ along the predetermined direction, β being an integer of 2 or more, and to yield such a lens effect that focal lengths for a plurality of incident beams of different wavelengths including the fundamental wavelength are equal to one another,

wherein the lens effect by the liquid crystal layer corresponds to a lens effect yielded by a Fresnel-lens,

wherein

a thickness d of the liquid crystal layer and refractive anisotropy of the liquid crystal molecules designed to satisfy the following expressions (1) to (3), and

a focal length f 0 at a fundamental wavelength λ 0 and a focal length f 1 at another wavelength (measured wavelength λ 1 ) different from the fundamental wavelength λ 0 are equal to each other,

φ m =2παβ[ m−r 2 /(2λ 0 f 0 β)]  (1),

φ m =2π(β+γ)[ m−r 2 /{2λ 1 f 1 (β+γ)}]  (2)

and

α=1+γ/β

wherein

r m <r<r m+1

α=λ 0 [Δn (λ 1 )−1]/{λ 1 [Δn (λ 0 )−1]}

β=Δ n (λ 0 ) d/λ 0

m= 0,1,2, . . . ,

where

r: distance from a central position of the liquid crystal lens as a Fresnel lens to an arbitrary position in the predetermined direction,

r m : distance from a central position of the liquid crystal lens as a Fresnel lens to a position corresponding to the mth Fresnel zone,

λ 0 : fundamental wavelength,

λ 1 : measured wavelength,

Δn(λ 0 ): difference in refractive index of the liquid crystal molecule at the fundamental wavelength λ 0 (difference between refractive indexes in two directions of the liquid crystal molecule, showing refractive anisotropy),

Δn(λ 1 ): difference in refractive index of the liquid crystal molecule at the measured wavelength λ 1 ,

f 0 : focal length at the fundamental wavelength λ 0 ,

f 1 : focal length at the measured wavelength λ 1 ,

d: thickness of the liquid crystal layer, and

γ: phase difference factor.

4. The liquid crystal lens according to claim 1 , wherein

the incident beam is polarized in a particular polarization direction, and

an in-plane alignment direction of the liquid crystal molecules under no application of voltage is parallel to the particular polarization direction.

5. The liquid crystal lens according to claim 1 , wherein the lens effect is such that focal lengths for a plurality of incident beams of different wavelengths within a visible wavelength range are equal to one another.

6. The liquid crystal lens according to claim 1 , wherein the lens effect is such that focal lengths for incident beams of three or more wavelengths are equal to one another, the three or more wavelengths including wavelengths of λ R , λ G and λ B belonging to respective wavelength ranges expressed by following expressions:

590 nm≦λ R ≦780 nm,

475 nm≦λ G ≦600 nm, and

400 nm≦λ B ≦490 nm.

7. A display device having a display unit for performing two-dimensional image display and a liquid crystal lens disposed opposite the display unit so that display image light from the display unit enters the liquid crystal lens, the liquid crystal lens comprising:

a first electrode,

a second electrode disposed opposite to the first electrode, and

a liquid crystal layer, including liquid crystal molecules having refractive anisotropy, disposed between the first electrode and the second electrode, the liquid crystal molecules being changed in alignment depending on voltage applied by the first electrode and the second electrode, thereby to form such a phase difference distribution that phase difference with respect to an incident beam of a fundamental wavelength varies from 0 to 2πβ along the predetermined direction, β being an integer of 2 or more, and to yield such a lens effect that focal lengths for a plurality of incident beams of different wavelengths including the fundamental wavelength are equal to one another,

wherein magnitude of voltage difference between the first electrode and the second electrode is varied in correspondence to the phase difference distribution along the predetermined direction.

8. The display device according to claim 7 , wherein

the lens effect of the liquid crystal lens is inactive under a condition that voltage difference between the first electrode and the second electrode is zero, and

two-dimensional display is performed through setting the lens effect of the liquid crystal lens to inactive state so that display image light from the display unit is transmitted without being refracted, whereas

three-dimensional display is performed through setting the lens effect of the liquid crystal lens to active state so that the display image light from the display unit is refracted so as to enable stereoscopy.

9. The display device according to claim 7 , wherein

display image light emitted from the display unit is polarized in a particular polarization direction to enter the liquid crystal lens as the incident beam, and

an in-plane alignment direction of the liquid crystal molecules under no application of voltage is parallel to the particular polarization direction.

10. The display device according to claim 7 , wherein

the display image light from the display unit contains three wavelength components of λ R , λ G and λ B belonging to respective wavelength ranges expressed by following expressions, and

the lens effect is such that focal lengths for incident beams of three or more wavelengths are equal to one another, the three or more wavelengths including wavelengths of λ R , λ G and λ B belonging to respective wavelength ranges expressed by following expressions:

590 nm≦λ R ≦780 nm,

475 nm≦λ G ≦600 nm, and

400 nm≦λ B ≦490 nm.