Phase-matched generation of coherent soft and hard X-rays using IR lasers
Phase-matched high-order harmonic generation of soft and hard X-rays is accomplished using infrared driving lasers in a high-pressure non-linear medium. The pressure of the non-linear medium is increased to multi-atmospheres and a mid-IR (or higher) laser device provides the driving pulse. Based on this scaling, also a general method for global optimization of the flux of phase-matched high-order harmonic generation at a desired wavelength is designed.
1. A method of generating coherent x-ray emission comprising the steps of:
(a) providing a gas as a nonlinear medium for high harmonic generation (HHG) of laser light;
(b) adjusting the pressure of the nonlinear medium to a selected pressure above one atmosphere;
(c) generating a laser driving pulse in the mid-IR region of the spectrum;
(d) focusing the driving pulse into the nonlinear medium to cause HHG upconversion into a coherent x-ray generated pulse;
(e) wherein steps (a) through (d) phase match the driving pulse and the generated pulse sufficiently to result in a coherence length much longer than the absorption depth.
2. The method of claim 1 wherein the laser pulse has a wavelength above 1 μm.
3. The method of claim 2 wherein the laser pulse has a wavelength of about 1.3 μm.
4. The method of claim 2 wherein the laser pulse has a wavelength of about 2 μm.
5. The method of claim 1 wherein the medium has moderate ionization levels between about 10 −3 % and 10%.
6. The method of claim 1 wherein the coherence length is at least about 1 mm.
7. The method of claim 6 wherein the coherence length is at least about 1 cm.
8. The method of claim 1 wherein the medium is one of the following: an atomic gas, a molecular gas, a mixture of atomic gases, a mixture of molecular gases, a mixture of atomic and molecular gases.
9. The method of claim 8 wherein the medium is one of the following: He, Ne, or Ar.
10. The method of claim 1 wherein the x-ray generated pulse has a wavelength falling in the soft x-ray region of the spectrum.
11. The method of claim 1 wherein the x-ray generated pulse has a wavelength falling in the water window region of the spectrum.
12. The method of claim 1 wherein the step of adjusting adjusts the pressure to at least multi-atmospheres.
13. The method of claim 1 further including the steps of injecting the medium within a hollow waveguide.
14. The method of claim 1 wherein the step of generating a pulse generates a pulse having a duration of between 3-300 fs and an energy of between 100 μJ and 1 J.
15. The method of claim 1 wherein the step of focusing the driving pulse generates a pulse having one of the following durations: femtosecond, attosecond, zeptosecond.
16. The method of claim 1 wherein the step of generating a pulse generates a pulse having a repetition rate between 1 Hz and 1 MHz.
17. A method for global flux optimization of coherent x-ray emission from a medium at a desired wavelength comprising the steps of:
(a) evaluating an index of refraction as a function of a range of wavelengths of a driving laser and an index of refraction of the corresponding generated light;
(b) evaluating HHG phase matching limits as a function of the laser wavelength;
(c) determining optimal laser parameters as a function of the laser wavelength;
(d) evaluating flux from a single emitter as a function of driving laser parameters under phase matching conditions;
(e) evaluating optimal density-length product as a function of the laser wavelength;
(f) combining steps (a)-(e) for the purpose of calculating macroscopic phase-matched coherent emission as a function of the wavelength of the generated light and the driving laser light;
(g) finding a global maximum of the flux at the desired HHG wavelength for the purpose of selecting optimal driving laser wavelength, optimal laser pulse parameters, optimal nonlinear medium and parameters of the nonlinear medium.
18. The method of claim 17 where the driving laser wavelength increases to values longer than the wavelength of the generated light for the purpose of optimizing phase matching of HHG at shorter wavelengths.
19. The method of claim 17 where the density-length product of the nonlinear medium increases as the driving laser wavelength increases.
20. The method of claim 17 where the global optimization is performed at the photon energy of the HHG phase matching limits.
21. The method of claim 1 further including the step of injecting the medium within a hollow waveguide.
22. The method of claim 21 , wherein the waveguide is tapered.
23. The method of claim 21 further including the steps of differentially pumping the medium from multiple atmospheres to vacuum near each end of the waveguide.
24. The method of claim 1 wherein the step of finding a global maximum of the flux is performed at a laser wavelength at the HHG phase matching limits.
25. The method of claim 1 further including the step of temporally shaping the driving pulse to mitigate group velocity mismatch.
26. The method of claim 1 further including the step of spatially shaping the driving pulse into a converging beam to mitigate group velocity mismatch.
27. The method of claim 1 further including the steps of temporally and spatially shaping the driving pulse to mitigate group velocity mismatch.