Apparatus for beam shaping of laser radiation

Abstract

An apparatus for beam shaping of laser radiation in the form of ultra short pulses includes an achromatic optical device comprising a first substrate having a first Abbe number and a second substrate connected to the first substrate and having a second Abbe number that is different from the first Abbe number. The first and second substrates are arranged to allow the laser radiation to at least partially pass through the first and second substrates in succession, wherein an optically functional transformation boundary surface is disposed on one of the first and second substrates. The optically functional transformation boundary surface allows the laser radiation to pass at least partially, such that a profile of the laser radiation is transformed into a top-hat profile.

Claims

1. An apparatus for beam shaping of laser radiation in the form of ultra short pulses, the apparatus comprising: an optically functional transformation boundary surface that allows the laser radiation to pass at least partially, such that a profile of the laser radiation is transformed into a top-hat profile; an achromatic optical device comprising a first substrate having a first Abbe number and a second substrate connected to the first substrate and having a second Abbe number that is different from the first Abbe number, the first and second substrates being arranged to allow the laser radiation to at least partially pass through the first and second substrates in succession, wherein the optically functional transformation boundary surface is disposed on one of each of the first and second substrates, such that the optically functional transformation boundary surface and the achromatic optical device together comprise a monolithic component.

2. The apparatus of claim 1, wherein the optically functional transformation boundary surface is an entry surface or as an emergence surface of one of the first and second substrates.

3. The apparatus of claim 1, wherein the optically functional transformation boundary surface is shaped to cause a transformation in the laser radiation from a Gaussian profile or a modified Gaussian profile into the top-hat profile.

4. The apparatus of claim 1, wherein the optically functional transformation boundary surface is shaped to cause a transformation into the top-hat profile for at least a first wavelength (λ.sub.1) and at least a second wavelength (λ.sub.2) that is different from the first wavelength (λ.sub.1) by more than 50 nm.

5. The apparatus of claim 4, wherein a shape of the optically functional transformation boundary surface is optimized for the first wavelength (λ.sub.1) and for the second wavelength (λ.sub.2) with respect to the transformation to be carried out.

6. The apparatus of claim 5, wherein optimization of the shape of the optically functional transformation boundary surface is achieved by minimizing the following function: $R=\int {.Math.\left[{\left(2/\sqrt{\pi }\right)}^{1/2}{e}^{-x^2}{e}^{i{\phi }_{{\lambda }_1}\left(x,y\right)}\right]-{\left(1/\alpha \right)}^{1/2}\mathrm{rect}\left(f/\alpha \right).Math.}^2\mathrm{df}+\int {.Math.\left[{\left(2/\sqrt{\pi }\right)}^{1/2}{e}^{-x^2}{e}^{i{\phi }_{{\lambda }_2}\left(x,y\right)}\right]-{\left(1/\alpha \right)}^{1/2}\mathrm{rect}\left(f/\alpha \right).Math.}^2\mathrm{df}$ where ℑ: Fourier transformation α: spatial scaling factor, f: frequency variable of the Fourier space, λ.sub.1: first wavelength, λ.sub.2: second wavelength, φλ.sub.1 and φλ.sub.2: phase distributions and x, y: coordinates of a coordinate system.

7. The apparatus of claim 1, wherein the optically functional transformation boundary surface is shaped to cause a transformation into the top-hat profile for at least a first wavelength (λ.sub.1) and at least a second wavelength (λ.sub.2) that is different from the first wavelength (λ.sub.1) by more than 100 nm.

8. The apparatus of claim 1, wherein the optically functional transformation boundary surface is shaped to cause a transformation into the top-hat profile for at least a first wavelength (λ.sub.1) and at least a second wavelength (λ.sub.2) that is different from the first wavelength (λ.sub.1) by more than 200 nm.

9. The apparatus of claim 1, wherein the optically functional transformation boundary surface is shaped to cause a transformation into the top-hat profile for a wavelength range of more than 50 nm in size.

10. The apparatus of claim 1, wherein the optically functional transformation boundary surface is shaped to cause a transformation into the top-hat profile for a wavelength range of more than 100 nm in size.

11. The apparatus of claim 1, wherein the optically functional transformation boundary surface is shaped to cause a transformation into the top-hat profile for a wavelength range of more than 200 nm in size.

12. The apparatus of claim 1, wherein at least one of the first and second substrates has at least one boundary surface that is curved aspherically.

13. The apparatus of claim 12, wherein the first and second substrates have mutually corresponding, curved surfaces on their sides facing one another, wherein the mutually corresponding, curved surfaces abut one another.

14. The apparatus of claim 1, wherein the first substrate comprises crown glass.

15. The apparatus of claim 1, wherein the second substrate comprises flint glass.

16. The apparatus of claim 1, wherein the first Abbe number is greater than 50 and the second Abbe number is less than 50.

17. The apparatus of claim 1, wherein the refractive index of the first substrate is less than 1.6.

18. The apparatus of claim 1, wherein the refractive index of the second substrate is greater than 1.6.

19. The apparatus of claim 1, wherein the apparatus is suitable for beam shaping of laser radiation in the form of pulses having a pulse length of less than 500 fs.

20. The apparatus of claim 1, wherein the first and second substrates have mutually corresponding curved surfaces on their sides facing one another, and wherein the mutually corresponding curved surfaces abut, and are permanently connected to, one another.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

(1) Other features and advantages of the present invention will become apparent from the following description of preferred exemplary embodiments with reference to the accompanying drawings.

(2) FIG. 1 is a side view in schematic form of an embodiment of an apparatus of the invention.

(3) FIG. 2 is an intensity distribution of a laser radiation that was transformed with an apparatus of the invention and that has a wavelength of 1,064 nm.

(4) FIG. 3 is an intensity distribution of a laser radiation that was transformed with an apparatus of the invention and that has a wavelength of 532 nm.

(5) Identical or functionally identical parts are provided with the same reference numerals in the figures.

DETAILED DESCRIPTION

(6) FIG. 1 shows an embodiment of an apparatus of the invention that comprises an achromatic optical device 1, which comprise a first substrate 2 and a second substrate 3.

(7) Furthermore, the apparatus comprises a transformation boundary surface 4 that is a part of the first substrate 1 and serves as the entry surface thereof. The optically functional transformation boundary surface 4 has a shape that can cause a laser radiation 10 passing through the optically functional transformation boundary surface (see FIG. 1) to be transformed from a Gaussian profile or a modified Gaussian profile into a top-hat profile.

(8) The first substrate 2 is made of crown glass and has an Abbe number greater than 50. The refractive index of the first substrate 2 may be between 1.5 and 1.6. The second substrate 3 is made of flint glass and has an Abbe number less than 50. The refractive index of the second substrate 3 may be between 1.6 and 2.0.

(9) The entry surface of the first substrate 1 is formed so as to be convex and may be curved aspherically, with the entry surface serving as the transformation boundary surface 4. The emergence surface 5 of the first substrate 2 is also convex and may be curved spherically, with the emergence surface being opposite the entry surface. As an alternative, there is the possibility that the emergence surface 5 is also curved aspherically.

(10) The entry surface 6 of the second substrate 3 is concave and may be curved spherically, with the entry surface facing the first substrate 2. As an alternative, there is the possibility that the entry surface 6 is also curved aspherically. The emergence surface 7 of the second substrate 3 is planar, with the emergence surface 7 being opposite the entry surface 6.

(11) In particular, the shape of the entry surface 6 of the second substrate 3 matches comparatively exactly the shape of the emergence surface 5 of the first substrate 2, so that these surfaces may abut one another in a precisely fitting manner. The mutually abutting surfaces are permanently connected to one another, for example, by adhesively bonding.

(12) There is certainly the possibility of switching the order of sequence of the substrates 1, 2, so that a substrate made of flint glass is provided on the left in FIG. 1; and a substrate made of crown glass is provided on the right in FIG. 1.

(13) Furthermore, there is the possibility that the transformation boundary surface is integrated into one of the other surfaces. Thus, for example, the emergence surface 7 of the second substrate 3 may be shaped such that it serves as the transformation boundary surface. There is also the possibility that the emergence surface 5 of the first substrate 2 and/or the entry surface 6 of the second substrate 3 is/are designed as the transformation boundary surface.

(14) In the illustrated exemplary embodiment, the shape of the transformation boundary surface 4 is optimized for two different wavelengths, i.e., for a first wavelength λ.sub.1=1,063 nm and for a second wavelength λ.sub.2=532 nm. There is certainly the possibility that the shape of the transformation boundary surface 4 is optimized for three or more different wavelengths.

(15) FIG. 2 shows in schematic form an intensity distribution 8 of a laser radiation 10, which has passed through the apparatus from left to right according to FIG. 1 and which has a wavelength of 1,064 nm. In this case the intensity distribution may be, for example, a far field distribution or may be focused into a working plane by a corresponding focusing optics. It has been found that the laser radiation has a top-hat profile.

(16) FIG. 3 shows in schematic form an intensity distribution 9 of a laser radiation 10, which has passed through the apparatus from left to right according to FIG. 1 and which has a wavelength of 532 nm. It has been found that the laser radiation also has a top-hat profile.

(17) The transformation boundary surface 4 is shaped such that a transformation into a top-hat profile takes place not only for the two wavelengths 532 nm and 1,064 nm, but that a corresponding transformation into a top-hat profile also takes place for laser radiations with wavelengths ranging in-between. Thus, the apparatus is suitable for the transformation of wide band ultra short laser pulses.

(18) Mathematically, the task of optimizing the transformation boundary surface 4 for two different wavelengths λ.sub.1 and λ.sub.2 can be solved in an iterative process by minimizing the functional R, reproduced below—here in a non-dimensional representation.

(19) $R=\int {.Math.\left[{\left(2/\sqrt{\pi }\right)}^{1/2}{e}^{-x^2}{e}^{i{\phi }_{{\lambda }_1}\left(x,y\right)}\right]-{\left(1/\alpha \right)}^{1/2}\mathrm{rect}\left(f/\alpha \right).Math.}^2\mathrm{df}+\int {.Math.\left[{\left(2/\sqrt{\pi }\right)}^{1/2}{e}^{-x^2}{e}^{i{\phi }_{{\lambda }_2}\left(x,y\right)}\right]-{\left(1/\alpha \right)}^{1/2}\mathrm{rect}\left(f/\alpha \right).Math.}^2\mathrm{df}$
where
ℑ: Fourier transformation
α: spatial scaling factor,
f: frequency variable of the Fourier space,
λ1: first wavelength,
λ2: second wavelength,
φλ1 and φλ2: phase distributions and
x, y: coordinates of a coordinate system.

(20) The minimization of the functional R results in the desired phase distributions φ.sub.λ1 and φ.sub.λ2, on the basis of which the shape of the transformation boundary surface is defined.

(21) Within the functional, the term (2/√{square root over (π)}).sup.1/2e.sup.−x.sup.2 represents the Gaussian intensity distribution of the input beam, to which a phase factor e.sup.iφ is multiplied up.

(22) In order to convert the phase modulation, impressed on the Gaussian beam, into the desired distribution of the output intensity, it is necessary for this term to undergo a Fourier transformation ℑ that is achieved, in practice, by a field generating Fourier transformation lens—also referred to as field lens for short.

(23) The term of the shape (1/α).sup.1/2 rect (f/α) corresponds to a representation of the top-hat-shaped target intensity distribution.

(24) The factor α is a parameter that determines the spatial dimension of the target field. By subtracting the terms of the transformed input intensity distribution from the target intensity distribution, the desired functionality of the transformation boundary surface is now ensured while minimizing the functional R.