Absolute calibration of the refractive index in photo-induced photonic lattices

Abstract

We demonstrate a method to experimentally calibrate the refractive index modulation in photorefractive lattices, a task rarely addressed that is crucial for quantitative comparisons of theories with experiments. We consider the linear propagation of a normally incident plane wave through simple lattices and its modulation amplitude at crystal output face. Finding no evidence of longitudinal (Talbot-like) oscillations, we discard an ideal propagation theory and construct a simple effective model that includes longitudinal relaxation. We obtain calibrations of 1D and 2D lattices consistent with standard theory in a high saturation regime. For 2D lattices, we find anisotropies χ = 1.5 − 2.5, stronger for smaller lattice period, and refractive indexes larger than for 1D lattices, also with more noise. Technol. 14, 423-428 (1996). 12. R. Magnusson and T. Gaylord, "Use of dynamic theory to describe experimental results from volume holography," J. Appl. Phys. 47, 190-199 (1976 oscillations are faster, we expect even stronger damping effects. 31. We take into account the finite resolution of our imaging system by convoluting the profiles given by the effective theory by a gaussian optical response of r.m.s width σ 0 = 0.80µm.

Anisotropic nonlinear refractive index measurement of a photorefractive crystal via spatial self-phase modulation

“…2(a)), defined as the ratio between the diameter of the outer ring along the k x -direction and along the perpendicular direction and averaged over the 10 images having the highest intensity (red-filled diamonds). We observe a very good agreement between the two methods used to estimate the anisotropy of the nonlinear crystal, and the value of 1.6 is coherent with the literature [17]. Moreover, our simulations indicate a slightly higher anisotropy of 2.0.…”

“…Both saturation intensity and maximum refractive index modification have been measured with respect to the input intensity, external voltage and incoherent illumination amplitude. We also clearly evidenced and measured the anisotropic nonlinear response of the crystal, in good agreement with reported measurement in lattices [17].…”

“…Moreover, when measured, the calibration method employed and the associated uncertainties are rarely addressed. Recently, Armijo et al proposed an absolute calibration method to measure the refractive index of photoinduced 1D and 2D photonic lattices [17]. These measurements are very consistent with theory but specific to lattice configurations in a focusing, highly saturated regime.…”

Photorefractive writing and probing of anisotropic linear and nonlinear lattices

“…The intensity distributions at the crystal output face are recorded on the real space CCD camera, and integrated in the x direction so that we consider only profiles I(y). To quantify the strength of the lattices, we use a fitting function, as in [8], of the form…”

“…2.a shows some examples of this procedure, for E 0 = 0, d = 10µm and different writing beam intensities I W . Our method for absolute calibration of ∆n 0 [8] then allows to convert the initial slope ∂α/∂t W into v 0 . For moderate lattice strengths ∆n 0 (which is often valid at short times), ∆n 0 is simply proportional to α.…”