METHOD FOR DESIGNING DIFFRACTIVE DEVICE AND METHOD FOR MANUFACTURING DIFFRACTIVE DEVICE
An embodiment is a method including calculating an electric field distribution of an emission light on an emission plane of the diffractive element with respect to the incident light, the incident light being a Gaussian beam, calculating an electric field distribution obtained by multiplying an electric field distribution of emission light from the emission plane by a Gaussian window in a plane parallel to the emission plane located at a predetermined distance from the emission plane, as an electric field distribution of a beam approximated by a Bessel Gaussian beam, calculating a first electric field distribution as an electric field distribution on the emission plane of the diffractive element with respect to the electric field distribution of the emission light on the plane, and determining a depth of an unevenness on a surface of the diffractive element.
1 - 5 . (canceled)
6 . A method for designing a diffractive element for modulating a phase of incident light, using a computer, the method comprising:
calculating an electric field distribution of an emission light on an emission plane of the diffractive element with respect to the incident light, the incident light being a Gaussian beam;
calculating an electric field distribution obtained by multiplying an electric field distribution of emission light from the emission plane by a Gaussian window in a plane parallel to the emission plane located at a predetermined distance from the emission plane, as an electric field distribution of a beam approximated by a Bessel Gaussian beam;
calculating a first electric field distribution as an electric field distribution on the emission plane of the diffractive element with respect to the electric field distribution of the emission light on the plane, on the basis of a principle of Kirchhoff's diffractive integral; 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.
7 . The method for designing the diffractive element according to claim 6 , further comprising:
calculating a second electric field distribution in which a positive square root of the light intensity distribution imaged on the plane is set as an intensity; and
calculating an electric field distribution on the emission plane of the diffractive element according to a convolution integral of the second electric field distribution and the first electric field distribution.
8 . The method for designing the diffractive element according to claim 6 ,
wherein in a Cartesian coordinate system in which the emission plane is orthogonal to a z-axis,
when calculating the electric field distribution of the emission light on the emission plane of the diffractive element, an electric field distribution E Ax (x, y) on the emission plane with respect to the incident light is calculated using equation (A), and
when calculating the electric field distribution obtained by multiplying the electric field distribution of emission light from the emission plane, an electric field distribution E BG, z1 (x, y) of the emission light on the plane is calculated by equation (B), using an electric field distribution E B, z1 (x, y) calculated using a diffractive integral of Kirchhoff.
E
Ax
(
x
,
y
)
=
e
-
(
r
xy
w
in
)
2
e
j
(
ar
xy
)
(
A
)
wherein, r xy =√{square root over ( )}(x 2 +y 2 ), win is a radius of a Gaussian beam,
α=k sin φ B , moreover, φ B is represented by following equation,
φ
B
=
sin
-
1
2.252728
2
r
B
k
=
sin
-
1
2.252728
4
r
B
π
λ
here, 2r B is a diameter of a Bessel beam, k is a wavenumber of the incident light or the emission light,
λ is a wavelength of the incident light or the emission light in the vacuum.
E
BG
,
z
1
(
x
,
y
)
=
e
-
(
r
xy
w
)
2
E
B
,
z
1
(
x
,
y
)
(
B
)
Here, w is a radius of the Gaussian window.
9 . The method for designing the diffractive element according to claim 6 ,
wherein a depth d(x, y) of unevenness on a surface of the diffractive element is expressed by equation (C).
d
(
x
,
y
)
=
λ
2
π
(
n
1
-
n
0
)
arg
(
E
BG
,
z
=
0
,
l
(
x
,
y
)
)
(
C
)
here, n 1 is a refractive index inside the diffractive element, no is a refractive index outside the diffractive element, λ is a wavelength in a vacuum of the incident light or the emission light, and arg(E B,z=0,1 (x, y) is a deviation angle of the electric field distribution on the emission plane of the diffractive element.
10 . A method for manufacturing a diffractive element comprising the method for designing the diffractive element according to claim 6 .
11 . The method for designing the diffractive element according to claim 7 ,
wherein in a Cartesian coordinate system in which the emission plane is orthogonal to a z-axis,
when calculating the electric field distribution of the emission light on the emission plane of the diffractive element, an electric field distribution E Ax (x, y) on the emission plane with respect to the incident light is calculated using equation (A), and
when calculating the electric field distribution obtained by multiplying the electric field distribution of emission light from the emission plane, an electric field distribution E BG,z1 (x, y) of the emission light on the plane is calculated by equation (B), using an electric field distribution E B,z1 (x, y) calculated using a diffractive integral of Kirchhoff.
E
Ax
(
x
,
y
)
=
e
-
(
r
xy
w
in
)
2
e
j
(
ar
xy
)
(
A
)
wherein, r xy =√{square root over ( )}(x 2 +y 2 ), win is a radius of a Gaussian beam,
α=k sin φ B , moreover, φ B is represented by following equation,
φ
B
=
sin
-
1
2.252728
2
r
B
k
=
sin
-
1
2.252728
4
r
B
π
λ
here, 2r B is a diameter of a Bessel beam, k is a wavenumber of the incident light or the emission light,
λ is a wavelength of the incident light or the emission light in the vacuum.
E
BG
,
z
1
(
x
,
y
)
=
e
-
(
r
xy
w
)
2
E
B
,
z
1
(
x
,
y
)
(
B
)
Here, w is a radius of the Gaussian window.
12 . The method for designing the diffractive element according to claim 7 ,
wherein a depth d(x, y) of unevenness on a surface of the diffractive element is expressed by equation (C).
d
(
x
,
y
)
=
λ
2
π
(
n
1
-
n
0
)
arg
(
E
BG
,
z
=
0
,
l
(
x
,
y
)
)
(
C
)
here, n 1 is a refractive index inside the diffractive element, n 0 is a refractive index outside the diffractive element, λ is a wavelength in a vacuum of the incident light or the emission light, and arg(E B,z=0,1 (x, y)) is a deviation angle of the electric field distribution on the emission plane of the diffractive element.
13 . The method of claim 7 further comprising:
manufacturing the diffractive element.
14 . The method of claim 13 , wherein manufacturing the diffractive element comprises:
forming a plate member of a transparent material;
designing a surface structure of the diffractive element based on the calculated electric field distribution on the emission plane of the diffractive element; and
forming the designed surface structure on a surface of the plate member using fine processing to create the unevenness on the surface of the diffractive element.
15 . The method of claim 14 , wherein the transparent material of the plate comprises of ZnS or quartz.