Two-photon absorption (TPA) is a promising technique for high density 3D-addressing for writing and read-out of data, provided that suitable two-photon sensitive materials facilitating fast recording and read-out will be developed. Free-base porphyrins and other metal-free tetrapyrroles, such as phthalocyanies and naphthalocyanines possess a unique fast intrinsic photo-tautomerization mechanism, which consists in switching the position of a pair of protons in the core of the molecule. In the past photo-tautomerization was used for holographic storage, but can be also applied for bit-oriented volumetric information storage using laser-excited fluorescence for readout. However, the utility of the photo-tautomerization for two-photon storage was severely restricted so far by the fact that all known tetrapyrroles have rather low TPA cross section, with values not exceeding 1 - 10 GM (1GM = 10-50 cm4 s photon-1). Recently we have discovered a new class of porphyrins, where TPA cross section is dramatically amplified by certain chemical modification of the chemical structure, and that some of the new porphyrins have the ability of photo-tautomerization by simultaneous absorption of two photons. In this paper we discuss the photophysics and nonlinear optics of the new porphyrins that can lead to fast volumetric re-writable optical storage. We present a quantitative comparison of the new compounds with previously known TPA chromophores and introduce a merit figure, which takes into account both TPA cross-section as well as the efficiency of light-induced changes. We show the combination of high cross sections of two-photon absorption, up to 1000 GM in near-IR range of wavelength, with the fast photo-tautomerization, offers, for the first time, a sufficiently high merit figure needed for implementation of high-density, high speed volumetric two-photon re-writable optical storage.