Method and arrangement for spectral broadening of laser pulses for non-linear pulse compression
A method and an arrangement of spectrally broadening laser pulses for non-linear pulse compression is disclosed which is based on the transition from the spectral broadening in a waveguide to the spectral broadening in a suitably shaped lens conductor. The arrangement is non-sensitive with respect to the variations of the pulse power, the position and parameters of the laser beam. The spectrally broadened pulses can be compressed in a satisfactory manner and the quality of the laser beam maintained by dividing the non-linear phase required for spectral broadening into sufficiently smaller steps which can be separated without non-linearity by suitable prorogation. The limitation of the pulse powers to less than the critical power of dielectrics is thus overcome and a pulse energy range for which the spectral broadening in the glass fibers cannot be used, is developed. The arrangement can compress pulses having a large average power.
1. Method for spectral broadening of laser pulses for non-linear pulse compression, in which the laser pulses are input into an optical arrangement in which they propagate alternatingly through at least one section containing at least one medium with non-linear optical properties, and in which the laser pulses are endowed with a non-linear phase through self-phase modulation, and at least one section in which substantially no non-linear phase is generated by self-phase modulation, wherein
the pulse power of the laser pulses is selected to be greater than the critical power of the medium with non-linear optical properties,
the non-linear phase of the laser pulses generated with each pass through the medium with non-linear optical properties is set by selection of the length of the medium and the intensity of the laser pulses to be so small that catastrophic self-focusing does not occur inside the medium,
the number of passes for producing the non-linear phase is at least 10 and is selected such that upon exiting the arrangement the laser pulses have a desired non-linear phase, and
the optical arrangement is dimensioned such that the Gouy parameter ψ of the arrangement, representing the Gouy phase acquired by the fundamental mode of the arrangement during propagation through the medium with non-linear optical properties and the section in which no non-linear phase is generated, lies neither in the middle nor directly on the edge of the stability range 0≦ψ≦π of the arrangement.
2. Method according to claim 1 , characterised in that the arrangement is dimensioned such that resonances of higher transverse modes are avoided, and the Gouy parameter ψ lies closer to the edge than the middle of the stability range.
3. Method according to claim 1 , characterised in that the arrangement is dimensioned such that the Gouy parameter ψ is between 0.03π and 0.24π or between 0.76π and 0.97π.
4. Method according to claim 1 , characterised in that the arrangement is dimensioned such that the Gouy parameter ψ for a non-linear phase of 2π acquired before exiting the arrangement lies between 0.81π and 0.97π and between 0.88π and 0.96π for a non-linear phase of 4π acquired before exiting the arrangement.
5. Method according to claim 1 , characterised in that the non-linear phase generated with each pass through the medium with non-linear optical properties is selected to be ≦π/10.
6. Method according to claim 1 , characterised in that the arrangement is dimensioned such that the Gouy parameter ψ for a non-linear phase of 8π acquired before exiting the arrangement lies between 0.90π and 0.97π, and the non-linear phase generated with each pass through the medium with non-linear optical properties is selected to be ≦π/20.
7. Method according to claim 1 , characterised in that a solid medium is used as the medium with non-linear optical properties.
8. Method according to claim 1 , characterised in that a gas-phase medium is used as the medium with non-linear optical properties.
9. Method according to claim 8 characterised in that the non-linear optical properties of the gas-phase medium are adjusted via the gas pressure.
10. Method according to claim 8 characterised in that a gas mixture of at least two different gases at atmospheric pressure is used as the gas-phase medium, and the non-linear optical properties of the gas-phase medium are set by means of the partial pressure of the two different gases.
11. Arrangement for spectral broadening of laser pulses for non-linear pulse compression, which has an optical fundamental mode and in which after they have been input the laser pulses propagate alternatingly through at least one section that contains at least one medium with non-linear optical properties and in which the laser pulses are endowed with a non-linear phase by self-phase modulation, and at least one section in which essentially no non-linear phase is produced by self-phase modulation, wherein
the length of the medium is selected such that the non-linear phase of the laser pulses generated with each pass through the medium with a pulse power that is greater than the critical power of the medium with non-linear optical properties is so small that catastrophic self-focusing does not occur inside the medium, and
the optical arrangement is dimensioned such that the number of passes for producing the non-linear phase is at least 10, and the Gouy parameter ψ of the arrangement, which represents the Gouy phase acquired by the fundamental mode during propagation through the medium with non-linear optical properties and the section in which no non-linear phase is generated, lies neither in the middle nor directly on the edge of the stability range 0≦ψ≦π of the arrangement.
12. Arrangement according to claim 11 , characterised in that the arrangement comprises at least two mirror elements, at which the laser pulses are reflected multiple times.
13. Arrangement according to claim 12 , characterised in that the arrangement is constructed as a multipass cell.
14. Arrangement according to claim 12 , characterised in that the medium is arranged as a non-linear element between the mirror elements.
15. Arrangement according to claim 12 , characterised in that at least one of the mirror elements includes a substrate of an optically transparent dielectric material, which has a highly reflective coating on a back side thereof, wherein the substrate serves as the medium with non-linear optical properties.
16. Arrangement according to claim 12 , characterised in that the mirror elements are furnished with a coating, through which at least a partial compensation is achieved for a dispersion the laser pulses experience when passing through the arrangement.
17. Arrangement according to claim 11 , characterised in that the medium with non-linear optical properties is a solid medium.
18. Arrangement according to claim 11 , characterised in that the medium with non-linear optical properties is a gas-phase medium.