## 1 Introduction
We reported porphyrin tetramers, composing of two butadiyne-linked porphyrin dimers, which were self-assembled by zinc to imidazolyl axial coordination, with a large value of 7600 GM employing femtosecond pulses at 870 nm (Scheme 4, top) [20,21]. A butadiyne bridge wasused to connect two porphyrins at their _meso_-positions, giving the molecule a planar configuration, which resulted in an expansion of the \(\pi\)-conjugation. Freebase porphyrins were also used for the terminals to increase polarization. In these studies, it is clear that the expansion of \(\pi\)-conjugation plays an important role in enhancing 2 PA. [PERSON] has also reported on the amplification of 2 PA in several ethynyl-bridged porphyrins reaching \(\sigma^{(2)}\) values of 9000 GM employing femtosecond pulses (Scheme 4, middle) [22; 23; 24; 25; 26]. To further expand conjugation in porphyrin analogs, [PERSON] has reported strong 2 PA in fused diporphyrins with \(\sigma^{(2)}\) values of around 15,000 GM [27]. The enhanced 2 PA is attributed to the completely flat dimerization of the adjacent porphyrins. Hexaphyrins bearing \(\sigma^{(2)}\) values of around 9900 GM at a longer wavelength of 1200 nm, due to the expanded aromatic structure, have also been reported by the same group [28; 29] (Scheme 4, bottom). **Scheme 3. ** Tetrapyrrolic 2 PA compounds. The molecules, without any reversible property, such as photochromism, which gives 0\(\leftrightarrow\)1 information transformation, may only provide read only memory (ROM) through a photobleaching process by two-photon irradiation, even though they exhibit high 2 PA efficiency. Photochromism is defined as the reversible transformation of chemical species. It is induced in one or both directions by the absorption of photon between two forms, A and B, having different absorption and/or emission properties (Scheme 5) [30]. The starting A can be converted to B by irradiation at wavelength \(\lambda_{1}\). B can revert to the first state, A, which is more thermodynamically stable, thermally or photochemically, by irradiation at wavelength \(\lambda_{2}\). In most cases, \(\lambda_{1}\) is shorter than \(\lambda_{2}\) and this phenomenon is known as positive photochromism. On the other hand, in some cases, \(\lambda_{1}\) is longer than \(\lambda_{2}\), which is known as inverse or negative photochromism. **Scheme 4. ** Porphyrinoids exhibiting large \(\sigma^{(2)}\) values. Some examples of photochromic compounds are shown in Scheme 6. There are two main categories in photochromism, namely, _cis-trans_ (_E/Z_) isomerizations and pericyclic reactions. _Cis-trans_ (_E/Z_) isomerization, for example, azobenzenes and thioindigos, involves a 180\({}^{\circ}\) rotation about a C=C double bond. The difference in the stereochemical orientation of substituents attached tothe double bond gives rise to divergence in absorption spectra between the _cis_ and _trans_ isomers. On the other hand, pericyclic reactions involve the ring opening and closing in the molecule. Spiropyrans [31], diarylethenes [32], and fulgides [33] are members of this category. **Scheme 6. ** The two types of mechanism in photochromic molecules. Photochromic compounds have potentials for development of optical devices such as memory, switch, and logic gate. The most promising candidates for high-density storage devices are photochromic compounds. Further, the key to producing high-density memories with photochromic compound is two-photon absorption. The following are required for the 2 PA-photochromic molecules; large 2 PA cross-sections, efficient photochromic reactivity, thermal stability of both isomers, and repetition durability. In this review, recent advances in two-photon absorbing photochromic molecules as potential materials for 3D optical memory are reviewed in chronological order. In particular, we focus on molecular materials, and, thereby, topics of devices, for example, laser system, optical system, and so on, which have been introduced in some excellent reviews [2,34], are not included.