Volume Fresnel zone plates fabricated by laser direct writing
A volume Fresnel zone plate and a method of producing such a device using a femtosecond laser for direct writing of zone plates. A volume zone plate has a number of Fresnel zone plate layers designed to focus light coherently to a single spot. Embodiments include both low numerical aperture (NA) and high NA zone plates, and provide a significant increase in overall diffraction efficiency over a single Fresnel zone plate.
1. A method of producing a volume Fresnel zone plate in a solid transparent material, comprising:
focusing a pulsed laser beam onto each of a set of points at a first depth within said solid transparent material so as to create a first Fresnel zone plate; and
focusing said pulsed laser beam onto each of a set of points at a second depth within said solid transparent material so as to create a second Fresnel zone plate,
wherein said first and second Fresnel zone plates are optically aligned with each other and include respective zones of different radii corresponding to different optical path lengths to a desired common focal point;
wherein said first and second Fresnel zone plates are fabricated using femtosecond laser direct writing; and
wherein said second Fresnel zone plate is at a greater depth than said first Fresnel zone plate and is created with less laser energy to maintain constant thickness of each zone plate.
2. The method of claim 1 , wherein each of said Fresnel zone plates is on the order of 100 μm thick and its separation distance from the other Fresnel zone plate is approximately twice its thickness.
3. The method of claim 2 , wherein said first Fresnel zone plate is on the order of 500 μm beneath the surface of said solid transparent material.
4. A volume modified Fresnel zone plate, comprising:
a solid transparent substrate with a substantially uniform base index of refraction;
a plurality of substantially parallel central-ring zone plates formed in said substrate, said zone plates each having a plurality of concentric rings with a refractive index different than said base index of refraction, said rings formed so as to produce substantially matched focusing at a desired focal point, said rings having substantially equal width but unequal radial spacing in each zone plate, the spacing between rings decreasing progressively with radius.
5. The volume modified Fresnel zone plate of claim 4 , wherein each ring has the width of a laser scanning line produced by a tightly focused femto second laser, and wherein each central-ring zone plate has low diffraction efficiency but works coherently with the other central-ring zone plates to improve the overall diffraction efficiency.
6. The volume modified Fresnel zone plate of claim 5 , wherein the width of each ring is less than approximately 5 μm.
7. The volume modified Fresnel zone plate of claim 6 , wherein the width of each ring is approximately 2 μm.
8. The volume Fresnel zone plate of claim 7 , wherein each of said central-ring zone plates is on the order of 100 μm thick and its separation distance from adjacent zone plates is approximately twice its thickness.
9. The volume Fresnel zone plate of claim 8 , wherein a shallower one of said central-ring zone plates is on the order of 500 μm beneath the surface of said solid transparent substrate.
10. The volume modified Fresnel zone plate of claim 4 , wherein said plurality of central-ring zone plates includes spaced first and second zone plates having first and second sets of substantially circular rings of radius r 1 and r 2 , respectively, and wherein the radius r 2 of a given ring in said second zone plate is a function of the radius r 1 of a corresponding ring in said first zone plate and of the spacing between said first and second zone plates.
11. The volume modified Fresnel zone plate of claim 10 ,
wherein said focal point is in a medium “a” with refractive index n a outside of said substrate and said substrate comprises a medium “b” with a refractive index n b ;
wherein the relationship between r 1 and r 2 is defined by
ϕ
1
=
ϕ
a
,
1
+
ϕ
b
,
1
=
2
π
λ
(
n
a
,
1
t
a
,
1
+
n
b
,
1
t
b
,
1
)
=
2
π
λ
m
1
+
b
1
(
1
)
ϕ
2
=
ϕ
a
,
2
+
ϕ
b
,
2
=
2
π
λ
(
n
a
,
2
t
a
,
2
+
n
b
,
2
t
b
,
2
)
=
2
π
λ
m
2
+
b
2
(
2
)
where
φ 1 =phase change from first zone plate to focal point
φ 2 =phase change from second zone plate to focal point
λ=wavelength
f=focal length
t=optical path length due to wave propagation
m=a whole number of wavelengths
b=phase remainder
and wherein a value of r 1 is determined for a given ring in said first zone plate, the phase remainder b 1 in Eq. (1) is calculated based on r 1 , said focal point and a given wavelength, and, in accordance with Eq. (2), a value is determined for the radius r 2 of a corresponding ring in said second zone plate which produces a phase remainder b 2 which substantially equals b 1 .
12. The volume modified Fresnel zone plate of claim 11 ,
wherein an initial value of r 1 is determined for each ring in said first zone plate based on a given wavelength and the distance to said focal point so as to produce substantially matched focusing at said focal point, and an initial value of r 2 is likewise determined for each ring in said second zone plate; and
wherein r 2 is adjusted from its initial value in accordance with said relationship between r 1 and r 2 defined in claim 11 .
13. The volume modified Fresnel zone plate of claim 11 , wherein medium “b” is glass.
14. A method of producing a volume Fresnel zone plate in a solid transparent material, comprising:
focusing a pulsed laser beam onto each of a set of points at a first depth within said solid transparent material so as to create a first Fresnel zone plate; and
focusing said pulsed laser beam onto each of a set of points at a second depth within said solid transparent material so as to create a second Fresnel zone plate,
wherein said first and second Fresnel zone plates are optically aligned with each other and include respective zones of different radii corresponding to different optical path lengths to a desired common focal point; and
wherein said first and second Fresnel zone plates are central-ring zone plates having first and second sets of substantially circular rings of radius r 1 and r 2 , respectively, and wherein the radius r 2 of a given ring in said second zone plate is a function of the radius r 1 of a corresponding ring in said first zone plate and of the spacing between said first and second zone plates.
15. The method of claim 14 ,
wherein said focal point is in a medium “a” with refractive index n a outside of said solid transparent material and said solid transparent material comprises a medium “b” with a refractive index n b ;
wherein the relationship between r 1 and r 2 is defined by
ϕ
1
=
ϕ
a
,
1
+
ϕ
b
,
1
=
2
π
λ
(
n
a
,
1
t
a
,
1
+
n
b
,
1
t
b
,
1
)
=
2
π
λ
m
1
+
b
1
(
1
)
ϕ
2
=
ϕ
a
,
2
+
ϕ
b
,
2
=
2
π
λ
(
n
a
,
2
t
a
,
2
+
n
b
,
2
t
b
,
2
)
=
2
π
λ
m
2
+
b
2
(
2
)
where
φ 1 =phase change from first zone plate to focal point
φ 2 =phase change from second zone plate to focal point
λ=wavelength
f=focal length
t=optical path length due to wave propagation
m=a whole number of wavelengths
b=phase remainder
and wherein a value of r 1 is determined for a given ring in said first zone plate, the phase remainder b 1 in Eq. (1) is calculated based on r 1 , said focal point and a given wavelength, and, in accordance with Eq. (2), a value is determined for the radius r 2 of a corresponding ring in said second zone plate which produces a phase remainder b 2 which substantially equals b 1 .
16. The method of claim 15 ,
wherein an initial value of r 1 is determined for each ring in said first zone plate based on a given wavelength and the distance to said focal point so as to produce substantially matched focusing at said focal point, and an initial value of r 2 is likewise determined for each ring in said second zone plate; and
wherein r 2 is adjusted from its initial value in accordance with said relationship between r 1 and r 2 defined in claim 15 .
17. The method of claim 16 , wherein r 2 is adjusted iteratively.