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arXiv:physics/0102032 · Journal of the Optical Society of America B

Two-photon absorption in potassium niobate

Andrew D. Ludlow, H. Mark Nelson, Scott Bergeson

Published Dec 1, 2001• 25 citations
arXivHTMLPDF

Abstract

We report measurements of thermal self-locking of a Fabry–Perot cavity containing a potassium niobate (KNbO3) crystal. We develop a method to determine linear and nonlinear optical absorption coefficients in intracavity crystals by detailed analysis of the transmission line shapes. These line shapes are typical of optical bistability in thermally loaded cavities. For our crystal we determine the one-photon absorption coefficient at 846 nm to be α=(0.0034±0.0022) m-1, the two-photon absorption coefficient at 846 nm to be β=(3.2±0.5)×10-11 m/W, and the one-photon absorption coefficient at 423 nm to be (13±2) m-1. We also address the issue of blue-light-induced infrared-absorption and determine a coefficient for this excited-state absorption process. Our method is particularly well suited to bulk absorption measurements where absorption is small compared with scattering. We also report new measurements of the temperature dependence of the index of refraction at 846 nm and compare with values in the literature.

DOI
10.1364/josab.18.001813

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We report measurements of thermal self-locking of a Fabry–Perot cavity containing a potassium niobate (KNbO3) crystal. We develop a method to determine linear and nonlinear optical absorption coefficients in intracavity crystals by detailed analysis of the transmission line shapes. These line shapes are typical of optical bistability in thermally loaded cavities. For our crystal we determine the one-photon absorption coefficient at 846 nm to be α=(0.0034±0.0022) m-1, the two-photon absorption coefficient at 846 nm to be β=(3.2±0.5)×10-11 m/W, and the one-photon absorption coefficient at 423 nm to be (13±2) m-1. We also address the issue of blue-light-induced infrared-absorption and determine a coefficient for this excited-state absorption process. Our method is particularly well suited to bulk absorption measurements where absorption is small compared with scattering. We also report new measurements of the temperature dependence of the index of refraction at 846 nm and compare with values in the literature.
The reflectivity of a single-channel waveguide mode upon resonantly coupling to a Kerr-active nonlinear resonant cavity is calculated analytically, including the effects of two-photon absorption. The resonant reflectivity takes the form of a Fano resonance because the solution includes linear reflections from perturbations downstream of the localized cavity. Instead of using a Hamiltonian formulation of the scattering problem, an intuitive set of basis states is used to expand the Green's function of the electric field wave equation. All resulting overlap functions describing the linear coupling between guided and localized states, and the nonlinear renormalization of the material's refractive index, are in terms of well-defined physical quantities. Although derived in the context of photonic crystal-based waveguides and cavities, the treatment is valid for any low-loss waveguide-resonator geometry that satisfies specific weak coupling criteria. For a cavity consisting of Al0.18Ga0.82As, hosting a localized mode at 1.55 microm with a Q of 4000 and a mode volume of 0.055 microm(3), we predict the onset of bistable reflection at incident powers of approximately 40 mW. The downstream reflections lead to hysteresis loops in the reflectivity that are topologically distinct from conventional Lorentzian-derived loops characteristic of isolated Fabry-Perot cavities. We provide a stability argument that reveals the unstable branches of these unique hysteresis loops, and we illustrate some of the rich bistable behaviors that can be engineered with such downstream sources.
Many authors have experimentally examined the nonlinearities of HgCdTe at resonance with the CO2 laser wavelength [1]. At room temperature non1inearities of electronic origin, arising from band filling, are weak because of Auger recombination and are masked by thermal effects. In this communication we extend the analysis of ref. 1 on thermally induced optical bistability at low power: we show, for the first time in HgCdTe, the appearance of clockwise hysteresis cycles in transmission as input power Pi is increased, due to nonlinear absorption. We can account for both absorptive and refractive nonlinear contributions by simultaneous monitoring of transmission and reflection. The Hg0.815Cd0.185Te plates (280 um in thickness, with doping pa =1*1016 cm-3, prepared and polished by Elettronica SpA) were placed without heatsinking in a thermally controlled environment. In Fig. 1 the transmitted (Pt) and reflected (Pr) power is shown as a function of Pi: the three data sets differ in cavity mistuning. The thermooptic effect was measured directly, by a close focus optical pyrometer, and indirectly by taking data at different thermal bath temperature T. The values of Pi at the hysteresis associated to a given cavity interference order (indicated with the symbols of Fig. 1c) drift with T (Fig. 2): the maximum induced temperature increase is inferred to be 30-35°C, with steps of 2.5-3.5°C at the switching points, and a value of dn/dT = -2.8*10-3 K-1 is deduced. Fig. 3 presents numerical results (to be compared with Fig. 1b) obtained parametrically solving the nonlinear Fabry Perot equations using the absorption measured after AR coating one sample face. This nonlinear absorption will be discussed in terms of a free carrier origin.
We present a theory of optical bistability for a Fabry-Perot cavity containing a medium with nonlinear refraction but linear absorption with only plane-wave and slowly varying envelope approximations. An analytic expression for the critical intensity Icfor the onset of bistability is derived and used to compare cavity designs. It is shown that 1) the important material parameter for minimum Icis the ration_{2}/\alpha 2) the limit to Icis set by limitations on finesse due to inhomogeneities rather than the absorption itself, and 3) the cavity design which gives lowest Icfor a given finesse is that for which the mirror transmissivity equals the absorption per pass; at high finesse this design leads to a total peak cavity transmission of 1/4 when mirror reflectivities are equal.
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