Calculations of the second-harmonic susceptibility tensor abc ͑−2 ; , ͒ are presented for bulk semiconductors within both the v · A and the r · E gauges. The description of the semiconductor states incorporates the "scissors" Hamiltonian commonly used to obtain the correct band gap. The nonlocality of the scissors correction leads to terms in abc ͑−2 ; , ͒ not considered before within a sum-over-states approach to the v · A gauge. Using this expression, we show that the results of the two gauges give the same result for abc ͑−2 ; , ͒, within very good numerical accuracy. As part of the derivation, we clarify the well-known result for the linear optical response which states that the scissors correction rigidly shifts the spectrum along the energy axis, keeping the line-shape intact. The calculation is presented for GaAs using an all-electron scheme and a pseudopotential scheme.
We propose and demonstrate a new type of metalenses that are phase compensated by gradient index (GRIN) or inhomogeneous permittivity metamaterials. Both elliptically and hyperbolically dispersive GRIN metalenses for both internal and external focusing are studied. The requirements for the GRIN metalenses and the light focusing characteristics are analyzed and numerically verified. The GRIN metalenses can achieve super resolution and have ordinary or extraordinary Fourier transform functions, thus enabling exotic applications.
We have studied the magnetic reversal and thermal stability of [Co(0.3 nm)/Pd(0.7 nm)]N multilayers patterned into 35-nm-diameter nanodot arrays. The short-time coercive fields are relatively constant with N while the room-temperature thermal stability parameter increases nearly linearly with N. However the magnetic switching volume extracted from the thermal stability is significantly less than the physical volume of the samples. The experimental results are in quantitative agreement with micromagnetic modeling, which indicates that reversal and thermal stability is controlled by nucleation and propagation of edge domains.
Magnetic nanowires supporting field-and current-driven domain wall motion are envisioned for new methods of information storage and processing. A major obstacle for their practical use is the domainwall velocity, which is traditionally limited due to the Walker breakdown occurring when the forcing field or current reaches a critical threshold value. We show through numerical and analytical modeling that the Walker breakdown limit can be extended or completely eliminated in antiferromagnetically coupled magnetic nanowires. These coupled nanowires allow for giant domain-wall velocities driven by field and/or current via spin transfer torque as compared to conventional nanowires.
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