Dispersion of bound electron nonlinear refraction in solids

Abstract

A two-band model is used to calculate the scaling and spectrum of the nondegenerate nonlinear absorption Aa(w,; wJ. From this, the bound electronic nonlinear refractive index n2 is obtained using a Kramers-Kronig transformation. We include the effects of two-photon and Raman transitions and the ac Stark shift (virtual band blocking). The theoretical calculation for n, shows excellent agreement with measured values for a five order of magnitude variation in the modulus of n2 in semiconductors and wide-gap optical solids. We also present new measurements of n, in semiconductors using the Z-scan method. The observed change of sign of n2 midway between the two-photon absorption edge and the fundamental absorption edge is also predicted. Thus, we now have a comprehensive theory that allows a determination of n2 at wavelengths beneath the band edge, given only the bandgap energy and the linear index of refraction. Such information is useful for a variety of applications including optical limiting, laser-induced damage, and all-optical switching. Some consequences for all-optical switching are discussed, and a wavelength criterion for the observation of switching is derived.

Bound-state third-order optical nonlinearities of germanium nanocrystals embedded in a silica host matrix

“…In general, bulk semiconductors change the sign of n 2 above their half E G values. 28 However, in Fig. 2 we observe that, in Ge NCs, this takes place at even beyond E G ; for the D = 2.25 and 3 nm NCs, the emergence of resonance is seen to develop, which can possibly reproduce this sign change at lower than E G values for the larger NCs.…”

“…Hence, as the figure of merit, n 2 / ␤ is proposed. 28 In our previous work, we have observed that the Si NCs possess much superior figure of merit parameters compared to bulk Si. 27 Figure 5 shows that Ge NCs closely resemble the results of Si NCs.…”

“…This negative sign of n 2 is known to be caused by both the two-photon absorption and the ac Stark effect. 28 In the size range considered in FIG. 1.…”

Femtosecond Z-scan measurements of nonlinear refraction in nonlinear optical crystals

“…Based on the two-band model with a simple direct bandgap, Sheike-Bahae et al [14] have calculated the dispersion and band-gap scaling of the bound electronic Kerr nonlinearity, n 2 , in solids. The nonlinear refractive index is given by…”

Two-Photon Quantum Dot Excitation during Optical Trapping

“…For CdSe illuminated with a wavelength of 1.06 µm, γ is found experimentally to be -1.47 × 10 -30 W µm -2 . 20 The theoretical estimates for polarizability are depicted in Figure 4, the black squares are based on simply using n as the refractive index in eq 2, and the black circles are based on using n c , which includes the nonlinear correction. As apparent from Figure 4, the absorption process that gives rise to the nonlinear contribution to the refractive index has only a minor effect on the total polarizability, R/ε 0 , found from eq 2.…”