METHOD FOR DESIGNING DIFFRACTIVE DEVICE AND METHOD FOR MANUFACTURING DIFFRACTIVE DEVICE
An embodiment is a method for designing a diffractive element which phase-modulates incident light including determining an electric field distribution on an emission plane with respect to a spherical wave condensed in a range between a first distance and a second distance from the emission plane, calculating a first electric field distribution as the electric field distribution on the emission plane by multiplying Exp[−jkz cos φ B ] by the electric field distribution for the spherical wave and integrating over the range, where z is a coordinate on a straight line, k is the wave number of emitted light, and φ B is a convergence angle between the emitted light and the straight line, and determining a depth of an unevenness on a surface of the diffractive element based on the calculated electric field distribution.
1 - 6 . (canceled)
7 . A method for designing a diffractive element which phase-modulates incident light using a computer, the method comprising:
determining an electric field distribution on an emission plane with respect to a spherical wave condensed in a range between a first distance and a second distance from the emission plane, on a straight line perpendicular to the emission plane of the diffractive element;
calculating a first electric field distribution as the electric field distribution on the emission plane of the diffractive element, by multiplying Exp [−jkz cos φ B ] when a coordinate on a straight line is z, the wave number of an emitted light from the emission plane is k, and a convergence angle that the emitted light makes with the straight line is φ B by the electric field distribution on the emission plane for the spherical wave, and by integrating over the range; and
determining a depth of an unevenness on a surface of the diffractive element on the basis of the electric field distribution on the emission plane of the diffractive element.
8 . A method for designing a diffractive element which phase-modulates incident light using a computer, the method comprising:
determining an electric field distribution on an emission plane with respect to a spherical wave condensed in a range between a first distance and a second distance from the emission plane, on a straight line perpendicular to the emission plane of the diffractive element;
calculating a first electric field distribution as the electric field distribution on the emission plane of the diffractive element, by multiplying Exp [−jkz cos φ B ] when a coordinate on a straight line is z, the wave number of an emitted light from the emission plane is k, and a convergence angle that the emitted light makes with the straight line is φ B by the electric field distribution on the emission plane for the spherical wave, and by adding over the range; and
determining a depth of an unevenness on a surface of the diffractive element on the basis of the electric field distribution on the emission plane of the diffractive element.
9 . The method for designing the diffractive element according to claim 7 , further comprising:
calculating a second electric field distribution which has a positive square root of the light intensity distribution imaged on a plane perpendicular to the straight line disposed in the range, as an intensity; and
calculating the electric field distribution on the emission plane of the diffractive element, by performing convolution integration of the second electric field distribution and the first electric field distribution.
10 . The method for designing the diffractive element according to claim 7 ,
wherein the first electric field distribution u 0 (x, y) is calculated by equation (A):
u
0
(
x
,
y
)
=
∫
z
α
z
β
u
0
,
z
(
x
,
y
)
·
e
-
jkz
cos
φ
dz
=
∫
z
α
z
β
ℱ
-
1
[
1
ℱ
[
g
(
x
,
y
)
]
]
·
e
-
jkz
cos
φ
dz
(
A
)
here, u 0′z (x, y) are the electric field distribution on the emission plane with respect
to the spherical wave condensed at the predetermined point, and z α and z β are
the first distance and the second distance, respectively, further, ϕ is expressed by the following equation.
φ
=
sin
-
1
2.252728
2
r
B
k
=
sin
-
1
2.252728
4
r
B
π
λ
Here, 2r B is a diameter of the Bessel beam, and λ is a wavelength of the emitted light.
11 . The method for designing the diffractive element according to claim 7 ,
wherein the depth d(x, y) of the unevenness on the surface of the diffractive element is expressed by equation (B).
d
(
x
,
y
)
=
λ
2
π
(
n
1
-
n
0
)
arg
(
u
0
,
l
(
x
,
y
)
)
(
B
)
Here, n, is a refractive index inside the diffractive element, no is a refractive index outside the diffractive element, λ is a wavelength of emitted light, and arg (u 0, 1 (x, y)) is a deflection angle of the electric field distribution on the emission plane of the diffractive element.
12 . The method of claim 7 further comprising:
manufacturing the diffractive element.
13 . The method for designing the diffractive element according to claim 8 , further comprising:
calculating a second electric field distribution which has a positive square root of the light intensity distribution imaged on a plane perpendicular to the straight line disposed in the range, as an intensity; and
calculating the electric field distribution on the emission plane of the diffractive element, by performing convolution integration of the second electric field distribution and the first electric field distribution.
14 . The method for designing the diffractive element according to claim 8 ,
wherein the first electric field distribution u 0 (x, y) is calculated by equation (A):
u
0
(
x
,
y
)
=
∫
z
α
z
β
u
0
,
z
(
x
,
y
)
·
e
-
jkz
cos
φ
dz
=
∫
z
α
z
β
ℱ
-
1
[
1
ℱ
[
g
(
x
,
y
)
]
]
·
e
-
jkz
cos
φ
dz
(
A
)
here, u 0′z (x, y) are the electric field distribution on the emission plane with respect
to the spherical wave condensed at the predetermined point, and z α and z β are
the first distance and the second distance, respectively, further, ϕ is expressed by the following equation.
φ
=
sin
-
1
2.252728
2
r
B
k
=
sin
-
1
2.252728
4
r
B
π
λ
Here, 2r B is a diameter of the Bessel beam, and λ is a wavelength of the emitted light.
15 . The method for designing the diffractive element according to claim 8 ,
wherein the depth d(x, y) of the unevenness on the surface of the diffractive element is expressed by equation (B).
d
(
x
,
y
)
=
λ
2
π
(
n
1
-
n
0
)
arg
(
u
0
,
l
(
x
,
y
)
)
(
B
)
Here, n 1 is a refractive index inside the diffractive element, no is a refractive index outside the diffractive element, λ is a wavelength of emitted light, and arg (u 0, 1 (x, y)) is a deflection angle of the electric field distribution on the emission plane of the diffractive element.
16 . The method of claim 8 further comprising:
manufacturing the diffractive element.
17 . The method of claim 12 , wherein manufacturing the diffractive element comprises:
providing a plate member of a transparent material;
forming a surface structure on the plate member by fine processing, wherein the surface structure corresponds to the depth of the unevenness determined for the diffractive element; and
wherein the transparent material is selected from the group consisting of ZnS and quartz.
18 . The method of claim 16 , wherein manufacturing the diffractive element comprises:
providing a plate member of a transparent material;
forming a surface structure on the plate member by fine processing, wherein the surface structure corresponds to the depth of the unevenness determined for the diffractive element; and
wherein the transparent material is selected from the group consisting of ZnS and quartz.