Systems and methods for spatiotemporal control of a laser and applications of same
Methods and systems are disclosed for using a chromatic lens system to provide a “flying focus”—i.e., an advanced focusing scheme enabling spatiotemporal control of a focal location. In a method, a photon beam is emitted from a source at a wavelength. The photon beam may have more than one wavelength. The photon beam is focused to a focal location using a chromatic lens system. The focal location is at a first longitudinal distance along an optical axis from the chromatic lens system. The wavelength of the photon beam is changed as a function of time to change the focal location as a function of time. The wavelength may be changed such that the focal location changes with a focal velocity.
1. A method of spatiotemporally changing a focal location of a photon beam as a function of time, comprising:
providing a photon beam emitted from a source wherein the photon beam has a wavelength (λ);
focusing the photon beam to a focal location using a chromatic lens system, the focal location is at a first longitudinal distance (z) along an optical axis from the chromatic lens system; and
changing the wavelength of the photon beam as a function of time to change the focal location as a function of time.
2. The method of claim 1 , wherein the photon beam has more than one wavelength and the chromatic lens system is selected to define a focal location for each wavelength which is different than the focal locations of other wavelengths.
3. The method of claim 1 , wherein the chromatic lens system is a diffractive lens.
4. The method of claim 3 , wherein the diffractive lens has a radially varying groove density
G
=
r
λ
0
f
0
,
where r is a radial distance from the optical axis, λ 0 is a central wavelength, and f 0 is a focal length at the central wavelength.
5. The method of claim 1 , wherein the wavelength is changed such that the focal location changes with a focal velocity (v).
6. The method of claim 5 , wherein the focal velocity is described by the equation:
v
(
z
)
c
=
[
1
+
(
d
λ
d
τ
)
-
1
(
dz
d
λ
)
-
1
c
]
-
1
wherein,
dz
d
λ
is a longitudinal dispersion of the chromatic lens,
d
λ
d
τ
is a rate of change of wavelength of the photon beam given by λ(τ), τ is a time-space coordinate where τ=t−z/c, t is time, and c is the speed of light.
7. The method of claim 1 , wherein the focal location (z) is changed over time (z(t))
by changing the wavelength of the photon beam according to
λ
(
τ
)
=
λ
0
[
1
-
z
(
τ
)
f
0
]
-
1
,
where the
chromatic lens system has a longitudinal dispersion given by
dz
d
λ
≅
-
f
o
λ
0
,
where λ 0 is a central wavelength and f 0 is a focal length at the central wavelength.
8. The method of claim 1 , wherein the source is a broadband laser.
9. The method of claim 8 , wherein the laser uses optical parametric chirped-pulse-amplification where
d
λ
d
τ
≅
Δ
λ
T
≅
constant
and Δλ is the laser's bandwidth and T is its total pulse length.
10. The method of claim 1 , wherein the wavelength of the photon beam is changed using one or more modulators to enable a rate of change in the laser frequencies to be changed to generate a nonlinear chirp.
11. The method of claim 1 , wherein the source is a plurality of single-wavelength lasers.
12. The method of claim 11 , wherein the plurality of single-wavelength lasers are combined using a grating to generate the photon beam.
13. The method of claim 1 , wherein the chromatic lens system comprises a chromatic refractive lens.
14. The method of claim 1 , wherein the chromatic lens system comprises a diffractive lens and a refractive lens.
15. The method of claim 1 , wherein a dispersion curve of the chromatic lens system is nonlinear.
16. An apparatus for providing a flying focus, comprising:
a photon beam source;
a chromatic lens system configured to receive a photon beam from the photon beam source and focus the photon beam at a focal location;
a controller configured to change a wavelength of the photon beam as a function of time to change the focal location as a function of time.
17. The apparatus of claim 16 , wherein the photon beam comprises more than one wavelength, and the controller changes the wavelength of the photon beam by selecting a subset of the wavelengths.
18. The apparatus of claim 17 , wherein the photon beam source is a broadband laser.
19. The apparatus of claim 18 , wherein the broadband laser uses optical parametric chirped-pulse-amplification.
20. The apparatus of claim 17 , wherein the photon beam source comprises a plurality of single-wavelength lasers.