Red dashed line shows centroid of the rocking curve up to laser fluence of 0. Above the saturation fluence, we observe a very interesting feature in the shapes of the diffraction peaks. As the incident laser power is increased further, the lattice expansion behavior resumes as it was shown in the un-doped data set.
However, unlike in the case of the un-doped GaAs, the appearance of the diffraction peak progressively becomes more asymmetric, and eventually above 0. The emergence of these two diffraction peaks implies that there are two distinct layers that carry different lattice parameters along the crystal depth. One of the de-convolved peaks is positioned at the Bragg condition of the GaAs crystal near equilibrium indicated by a black dashed line while the other continuously shifts toward smaller angles as marked by the red dashed line. This is also consistent with TPA, which is mostly confined to the regions of highest fluence near the surface.
The early onset of SPA saturation in the n-doped sample results in a narrower diffraction peak, allowing the onset of TPA to be more readily observed modifications of the peak shape. Consequently, we are visualizing the nonlinear progression of crystal lattice behaviors, during which its optical properties are changed from initially opaque to transparent to even more opaque. A subtle but important feature can be found in the diffraction peak profile at a laser fluence of 0. Such observation implies an additional layer that is even more opaque, which may be attributed to higher order optical absorption processes.
We plan to re-visit details of this phenomena in future.
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Coincidently, it is very interesting to note that similar fluence-dependent lattice behavior has been previously reported by Basak et al. Also closely related to this work, Kadlec et al. In summary, we performed TRXS measurements with sub-atomic length scale precision on the combined effects of strain saturation and complementary TPA effects in a solid by using synchrotron x-rays. We find that the deformation potential scattering is the fundamental and dominant reason for the impulsive responses of the lattice to the laser during the presence of a dense population of free carriers in GaAs.
We also demonstrate multiple distinct crystal lattice behaviours can be manifested due to SPA, saturable absorption, and TPA. The quantitative agreement existing between the 0 0 4 reflection data sets and the simulation supports this interpretation. At even higher laser fluences, we would expect the significant amount of transverse kinetic energy present to enhance both nonlinear and anisotropic properties such as the deformation potential tensor and phonon softening We may also gain new physical insights from studying systems with very different electronic behaviors such as indirect bandgap semiconductors or semiconductors with even faster recombination times such as InSb.
Finally, the extension of these methods to sub-picosecond x-ray capabilities at XFELs 45 , 46 should allow the study of the intervalley transition process 48 , which takes place in time scales that are much faster than what can be resolved with x-rays from storage ring based sources. Synchrotron TRXS was performed at Beamline 7ID of the Advanced Photon Source 33 where a water-cooled double-crystal diamond 1 1 1 monochromator combined with horizontal-plane focusing and vertical slits provided a collimated, micron square keV x-ray beam on the semiconductor sample.
Before and after the diffraction measurements, knife-edge scans of both laser and x-ray beams at the sample position verified that the laser uniformly overfilled the x-ray spot with a 5-mm FWHM smooth spatial profile. With the use of four-circle diffraction geometry, the sample was oriented in the x-ray beam such that the 0 0 4 reflection was measured near its intrinsic angular resolution. Absorbing filters were also placed on the detector arm to reduce the x-ray intensity so that an extended dead-time model 49 could be used for dead-time correction and error estimation.
We employ a one-dimensional carrier-driven strain model 43 for laser-induced strain generation and propagation inside a GaAs bulk crystal. In our model, two assumptions are made: i the energy relaxation from femtosecond irradiation to creating free-carrier population takes place instantaneously, and ii the electron-hole pairs relay their energy immediately to the lattice.
These are reasonable assumptions for the simulation because such processes take place within a few picoseconds, which is well beyond the time-resolution available at storage-ring based x-ray synchrotrons. We assume that the energy difference between the laser photon energy and the electronic-energy bandgap of the material i. Subsequent transient removal of excess carriers and diffusion of carriers and heat are characterised as follows:. Rapid expansion of the lattice near the surface launches two counter propagating compression waves along the surface normal direction, resulting in coexistence of relatively slow-decaying electronic strain and two-mobile strains within a few nanosecond time-scale.
To calculate the shift and shape evolution of the x-ray diffraction patterns for each laser fluence, we follow the numerical formulation initially derived by Wie et al. Tables 1 and 2 shows the list of parameters for the semiconductor material and x-ray scattering that are used for the simulation.
How to cite this article : Williams, G. Direct measurements of multi-photon induced nonlinear lattice dynamics in semiconductors via time-resolved x-ray scattering. Publisher's note: Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. Zhang, H. Molybdenum disulfide MoS 2 as a broadband saturable absorber for ultra-fast photonics. Barbay, S. Excitability in a semiconductor laser with saturable absorber. Manolatou, C.
All-optical silicon modulators based on carrier injection by two-photon absorption. Jin, C. Photonic switching devices based on semiconductor nano-structures. Journal of Physics D: Applied Physics 47 , — He, R. Integration of gigahertz-bandwidth semiconductor devices inside microstructured optical fibres.