RESEARCH LETTER The signal gain that we expect as c ared to normal RIXS or XES al Spin-o we 4 45.82-52012 yields tor K and L shells J.Phy the other hand,dire the maiority of the 9. meter)havea 0 nel,S.Cohe 11.Mukcar 23511020 nt we did observe traces 01258 mized X-rayo SLAc Tec B.D Meno Park Gel'mukh on of a strong x-ra tudies with cons probe be ues,hug s in the utrafast tim 166 10emP136.1741i72012 small signals from extremely dilute active centres can now be dissecte 17 METHODS SUMMARY 18 eneth free-electror the 9 20 5.456-4572011 ron 481,4 2012 50.fe.l he beam Spectra XE with ar anda 25 d at an angle ol 27. emera Natur 11510 Mon ch bin. 29. 110(2000 FllMethodsandanyasociatodretierencsarearalatbleintheonineversionot d J.Stohr for disc 0 201. n by the nd ext dy inte Author 3 103.0474012D0 manusript waswbyMBthinut fromall van den Author nfor nformation is 83.7 5 The signal gain that we expect as compared to normal RIXS or XES experiments stems from two sources. On one hand, the saturation of stimulated emission is an indicator that most core holes decay via the emission of photons instead of decaying via Auger processes. This pushes the observed fluorescence yield from the 1023 level in the direction of unity. On the other hand, directing the majority of the emission towards the detector can substantially increase the signal, given that typical fluorescence detectors (and our spectrometer) have a geometrical acceptance of less than 1024 of the full solid angle. There￾fore, stimulated emission can enhance the detected signal by several orders of magnitude. In our experiment we did observe traces of sample damage. Generally though, with optimized geometries at opti￾mized X-ray sources, the signal gain can be used to minimize acquisi￾tion times in the non-damaging regime, or alternatively to record full spectra in a single X-ray shot, so that the spectroscopic information is essentially generated before X-ray-induced changes set in. Such enhanced signal levels enable highly selective RIXS and XES studies with considerably improved energy resolution, so that new low￾energy excitations may be discovered. Through the combination with pump–probe techniques, huge parameter spaces in the ultrafast time domain can quickly bemapped. Finally, through the combination of non￾linear techniques from optical lasers with the high specificity of X-rays, small signals from extremely dilute active centres can now be dissected. METHODS SUMMARY Photon parameters. The experiments were conducted at the free-electron laser FLASH at Hamburg, Germany, operating at a photon energy of 115 eV. The spec￾trally resolved data was recorded at a repetition rate of 5 Hz with 30-fs pulses17,27. We used the grating of beamline PG 2 as a mirror28. The focus was round with a diameter of 45 mm, leading to fluences up to 1 J cm22 . The angular dependence was measured at beamline BL 2 (ref. 29) at a burst repetition rate of 10 Hz, each inclu￾ding 100 pulses at 250 kHz. The focal size was adjusted to be about 40 mm to com￾pensate for the now 50-fs-long pulses. With a gas attenuator, we set the fluence around 1 J cm22 . The incoming photon numbers have been measured for each shot by a gas monitor detector29. Experimental setup.We scanned hydrogen-passivated silicon (100) surfaces through the beam. Spectra were recorded with a Scienta XES 355 spectrometer30 and a single￾photon-counting, multi-hit-capable detector centred at 92 eV with a resolution of 0.4 eV. The scattering plane was the horizontal plane of polarization of the incom￾ing photons with the spectrometer at around 85u to the beam (15u to the sample surface), while the pulses impinged at an angle of 80uto the surface. For the angu￾lar dependence, we used an avalanche photodiode with an aluminiumfilter to block optical light. 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Author Contributions All authors contributed to planning parts of the experiment. Research was conducted by F.S., C.T., N.P., C.S.-L. and M.B. Data analysis and interpretation was done by M.B., S.S. and A.F. The formalism was developed and the manuscript was written by M.B. with input from all co-authors. Author Information Reprints and permissions information is available at www.nature.com/reprints. The authors declare no competing financial interests. Readers are welcome to comment on the online version of the paper. Correspondence and requests for materials should be addressed to M.B. (martin.beye@helmholtz-berlin.de). RESEARCH LETTER 4 | NATURE | VOL 000 | 00 MONTH 2013 ©2013 Macmillan Publishers Limited. All rights reserved