Limitation due to three-photon absorption on the useful spectral range for nonlinear optics in AlGaAs below half band gap

Abstract

We report measurements of the spectral dispersion and the magnitude of three-photon absorption in Ale,sGa,,s,As for photon energies between one half and one third the band gap and show that a two-parabolic-band model is valid in this material. These results indicate that there is a limited spectral range below half the band gap in AlGaAs (and presumably all semiconductors) in which the bound electronic optical nonlinearity can be used without significant multiphoton absorption.One of the hardest aspects of nonlinear optics is finding a suitable nonlinear material for various applications. For example, we have been interested in all-optical waveguide switching devices which require solid-state materials that exhibit a large, ultrafast third-order nonlinear response with little or no absorption at the communication wavelengths of 1.3 and 1.55 ,UIL There are many materials with a large third-order nonlinear response but the major problem has been excessive absorption. The total absorption can have a number of contributions so that (Y= czr + c@= (Y$ + . . . . where a2 and cr, are the two-(2PA) and three-(3PA) photon absorption coefficients, respectively, and I is the intensity. For example, 2PA in semiconductors between the band gap and half the band gap is known to be detrimental to alloptical switching.' Below half band gap the 2PA coefficient decreases rapidly with increasing wavelength so that the two-photon figure of merit T-Cl, as required.lY2 AtGaAs, when used with photons of energy just less than half the band-gap energy, was found to be an ideal material for alloptical switching, leading recently to subpicosecond waveguide switching with 65-pJ energies.3'4 However, when an AlGaAs device is operated at wavelengths too far below half the band gap, 3PA appears to become a limiting factor for all-optical switching.'There are a number of detailed calculations which have been made on multiphoton absorption in different materials based on models of varying sophistication.6*7 There is now a wealth of 2PA data available for comparison with theory.* In particular, a simple analysis using a two-parabolic-band model by Wherrett has provided a reasonable prediction of 2PA coefficients for semiconductor materials, including AlGaAs."@ For 3PA, experimental data is very limited. No spectral dispersion has been reported and agreement with existing theories is unclear. For AlGaAs in particular, a single value for CL-+ has been published near 1.67 pm, which agrees within a factor of two with theory3 In this letter, we report measurements of the spectral dispersion and magnitude of LU, below half the band gap, show that it agrees well with Wherrett's two-parabolic-band model, and evaluate the spectral range over which AlGaAs can be used for efficient nonlinear optics.The 3PA coefficient can be calculated from Eq. Ref. 6:(1) in where P is the Kane parameter, E, the band-gap energy, hw the energy of the photon, n is the refractive index of the material, and e'/& the fine-structure constant. For these calculations the wavelength d...

Three-photon absorption in ZnO and ZnS crystals

“…In particular, the 3PA spectra and n 2 wavelength dispersions are probed in detail with both femtosecond Z-scan and timeresolved pump-probe techniques. We have found that the 3PA spectra of wide-gap semiconductors fit well to a model developed by Brandi and de Araujo [19], contradicting the results for narrow-band-gap semiconductors [14]. This paper is organized as follows.…”

“…A 3PA coefficient measured by Catalano et al is also added for comparison [17]. It is interesting to note that for AlGaAs semiconductor, the Wherrett's theory is experimentally verified to be more accurate [14]. Fig.…”

“…Nonlinear absorption is not wanted as it may attenuate beam before the required nonlinear phase shift is achieved. In order to quantify the effects of 3PA, the nonlinear figure of merit (FOM) has been formulated [14], where [12]. All the results are listed in Table 1.…”

“…The implementation of such devices requires materials with low linear and nonlinear losses, high Kerr-type refractive nonlinearities and response times of a few picoseconds or less [11]. To search for materials which meet the above requirements, it has been suggested to target at semiconductors with their band gap at least twice the photon energy used (E g > 2 E photon ) avoiding optical absorption due to one-or two-photon transitions [12][13][14]. In this regard, wide-gap semiconductors are a suitable candidate; and ZnSe has been recently reported to be one of the promising candidates [15].…”

Lorentzian model for nonlinear switching in a microresonator structure

“…We have chosen to expand rðxÞ instead of tðxÞ because expanding rðxÞ gives us a closer resemblance to the Lorentzian lineshape under the same approximation ðd/ðxÞ ( 1Þ. In the absence of nonlinearity (n 2 ¼ 0), (11) and (13) give a simple Lorentzian model for the transmission and reflection of the structure [8]. In Fig.…”