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We have theoretically studied the field-strength dependent high-harmonic generation (HHG) in doped systems like nano-size or bulk materials. Our results show when the amplitude of the vector potential A_peak of the driving laser reaches the half-width of the Brillouin zone ({\pi}/a0), the harmonic yield of the undoped systems is larger than the doped systems. The band-climbing process enhances the interband transition of HHG for higher conduction bands. When A_peak is below {\pi}/a0 , the harmonic yield of the doped systems is stronger than the undoped systems. The atomic doping density also influences the field-strength dependent spectra., Comment: 10 pages

Various interference effects are known to exist in the process of high harmonic generation (HHG) both at the single atom and macroscopic levels. In particular, the quantum path difference between the long and short trajectories of electron excursion causes the HHG yield to experience interference-based temporal and spectral modulations. In solids, due to additional phenomena such as multi-band superposition and crystal symmetry dependency, the HHG mechanism appears to be more complicated than in gaseous atoms in identifying accompanying interference phenomena. Here, we first report experimental data showing intensity-dependent spectral modulation and broadening of high harmonics observed from bulk sapphire. Then, by adopting theoretical simulation, the extraordinary observation is interpreted as a result of the quantum path interference between the long and short electron/hole trajectories. Specifically, the long trajectory undergoes an intensity-dependent redshift, which coherently combines with the short trajectory to exhibit spectral splitting in an anomalous way of inverse proportion to the driving laser intensity. This quantum interference may be extended to higher harmonics with increasing the laser intensity, underpinning the potential for precise control of the phase matching and modulation even in the extreme ultraviolet and soft X-ray regime. Further, this approach may act as a novel tool for probing arbitrary crystals so as to adjust the electron dynamics of higher harmonics for attosecond spectroscopy.